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Chapter 53: Surface Area of Prisms and Cylinders

Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 7Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Surface Area of Prisms and Cylinders with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Unit Rate (a rate per one unit)
  • Surface Area (total area of the outside of a 3D object)
  • Estimate (a close approximation used to check whether an answer is reasonable)
  • Solution (a value or result that satisfies the problem)
  • Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
  • Reasonableness (whether an answer makes sense in the context of the problem)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

53.1 Three-dimensional objects

Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Explain Three-dimensional objects in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Three-dimensional objects becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Three-dimensional objects and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Three-dimensional objects becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Three-dimensional objects using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Three-dimensional objects becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Three-dimensional objects problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Three-dimensional objects becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Three-dimensional objects could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Three-dimensional objects becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Three-dimensional objects. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.2 Faces

Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Explain Faces in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Faces becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Faces and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Faces becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Faces using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Faces becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Faces problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Faces becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Faces could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Faces becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Faces. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.3 Edges

Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Explain Edges in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Edges becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Edges and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Edges becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Edges using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Edges becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Edges problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Edges becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Edges could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Edges becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Edges. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.4 Vertices

Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Explain Vertices in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Vertices becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Vertices and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Vertices becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Vertices using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Vertices becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Vertices problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Vertices becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Vertices could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Vertices becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Vertices. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.5 Nets

Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Nets. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.6 Surface area

Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area .

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area .

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area .

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area .

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area .

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Surface area. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.7 Rectangular prisms

Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Convert 0.5 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 0.5 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 50 cm

Worked Example 7

Problem: Convert 1.2 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 1.2 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 120 cm

Worked Example 8

Problem: Convert 2.75 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 2.75 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 275 cm

Worked Example 9

Problem: Convert 3.6 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 3.6 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 360 cm

Worked Example 10

Problem: Convert 4.05 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 4.05 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 405 cm

Practice Exercise

Create one new question about Rectangular prisms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.8 Triangular prisms

Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Convert 0.5 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 0.5 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 50 cm

Worked Example 7

Problem: Convert 1.2 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 1.2 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 120 cm

Worked Example 8

Problem: Convert 2.75 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 2.75 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 275 cm

Worked Example 9

Problem: Convert 3.6 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 3.6 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 360 cm

Worked Example 10

Problem: Convert 4.05 metres to centimetres.

  1. Use 1 m = 100 cm.
  2. Multiply 4.05 by 100.

Very beginner explanation: Metric conversions use powers of 10.

Answer: 405 cm

Practice Exercise

Create one new question about Triangular prisms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.9 Cylinder parts

A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts .

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts .

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts .

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts .

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts .

Answer: 678.58 cm²

Worked Example 6

Problem: Find the volume of a cylinder with radius 2 cm and height 5 cm.

  1. Use V = πr²h.
  2. V = π(2)²(5).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 62.83 cm³

Worked Example 7

Problem: Find the volume of a cylinder with radius 3 cm and height 6 cm.

  1. Use V = πr²h.
  2. V = π(3)²(6).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 169.65 cm³

Worked Example 8

Problem: Find the volume of a cylinder with radius 4 cm and height 7 cm.

  1. Use V = πr²h.
  2. V = π(4)²(7).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 351.86 cm³

Worked Example 9

Problem: Find the volume of a cylinder with radius 5 cm and height 8 cm.

  1. Use V = πr²h.
  2. V = π(5)²(8).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 628.32 cm³

Worked Example 10

Problem: Find the volume of a cylinder with radius 6 cm and height 9 cm.

  1. Use V = πr²h.
  2. V = π(6)²(9).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 1017.88 cm³

Practice Exercise

Create one new question about Cylinder parts. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.10 Cylinder net

A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net .

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net .

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net .

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net .

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net .

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Cylinder net. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.11 Lateral area of cylinder

A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder .

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder .

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder .

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder .

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder .

Answer: 678.58 cm²

Worked Example 6

Problem: Find the volume of a cylinder with radius 2 cm and height 5 cm.

  1. Use V = πr²h.
  2. V = π(2)²(5).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 62.83 cm³

Worked Example 7

Problem: Find the volume of a cylinder with radius 3 cm and height 6 cm.

  1. Use V = πr²h.
  2. V = π(3)²(6).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 169.65 cm³

Worked Example 8

Problem: Find the volume of a cylinder with radius 4 cm and height 7 cm.

  1. Use V = πr²h.
  2. V = π(4)²(7).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 351.86 cm³

Worked Example 9

Problem: Find the volume of a cylinder with radius 5 cm and height 8 cm.

  1. Use V = πr²h.
  2. V = π(5)²(8).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 628.32 cm³

Worked Example 10

Problem: Find the volume of a cylinder with radius 6 cm and height 9 cm.

  1. Use V = πr²h.
  2. V = π(6)²(9).

Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.

Answer: 1017.88 cm³

Practice Exercise

Create one new question about Lateral area of cylinder. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.12 Surface area of cylinder

Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder .

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder .

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder .

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder .

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder .

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

  1. Find the areas of the three different face pairs.
  2. SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Surface area of cylinder. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.13 Square units

Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: State one defining/property clue for a Square.

  1. 4 equal sides; 4 right angles

Very beginner explanation: Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Use the listed property to classify the shape.

Worked Example 2

Problem: State one defining/property clue for a Rectangle.

  1. opposite sides equal; 4 right angles

Very beginner explanation: Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Use the listed property to classify the shape.

Worked Example 3

Problem: State one defining/property clue for a Parallelogram.

  1. opposite sides parallel and equal

Very beginner explanation: Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Use the listed property to classify the shape.

Worked Example 4

Problem: State one defining/property clue for a Rhombus.

  1. 4 equal sides; opposite angles equal

Very beginner explanation: Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Use the listed property to classify the shape.

Worked Example 5

Problem: State one defining/property clue for a Trapezoid.

  1. at least one pair of parallel sides

Very beginner explanation: Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Use the listed property to classify the shape.

Worked Example 6

Problem: Explain Square units in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Square units and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Square units using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Square units problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Square units could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Square units. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

53.14 Packaging applications

Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈87.96.

Very beginner explanation: Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈169.65.

Very beginner explanation: Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈301.59.

Very beginner explanation: Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈471.24.

Very beginner explanation: Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

  1. Use SA=2πr²+2πrh.
  2. SA≈678.58.

Very beginner explanation: Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Explain Packaging applications in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Packaging applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Packaging applications and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Packaging applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Packaging applications using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Packaging applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Packaging applications problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Packaging applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Packaging applications could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Packaging applications becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Packaging applications. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

Chapter Notes, Practice, and Common Mistakes

Chapter Notes

  • Read the complete question before choosing an operation, formula, graph, or model.
  • Write technical words together with their meaning until you are comfortable using them.
  • Show all important steps so another student can follow your reasoning.
  • Keep units, labels, signs, axes, variables, and mathematical symbols clear.
  • Estimate before or after calculating when an estimate can help check reasonableness.
  • For real-life problems, explain what the final number means in the situation.

Extra Practice

  1. Create and solve a new question about Three-dimensional objects . Show your reasoning and check your answer.
  2. Create and solve a new question about Faces . Show your reasoning and check your answer.
  3. Create and solve a new question about Edges . Show your reasoning and check your answer.
  4. Create and solve a new question about Vertices . Show your reasoning and check your answer.
  5. Create and solve a new question about Nets . Show your reasoning and check your answer.
  6. Create and solve a new question about Surface area . Show your reasoning and check your answer.
  7. Create and solve a new question about Rectangular prisms . Show your reasoning and check your answer.
  8. Create and solve a new question about Triangular prisms . Show your reasoning and check your answer.
  9. Create and solve a new question about Cylinder parts . Show your reasoning and check your answer.
  10. Create and solve a new question about Cylinder net . Show your reasoning and check your answer.
  11. Create and solve a new question about Lateral area of cylinder . Show your reasoning and check your answer.
  12. Create and solve a new question about Surface area of cylinder . Show your reasoning and check your answer.

Common Mistakes

  • Assuming a diagram is drawn to scale.
  • Confusing radius and diameter.
  • Using square units for volume or cubic units for area.
  • Applying a scale factor to only one dimension.
  • Forgetting the circular bases in cylinder surface area.
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30 Review Questions and Answers

Q1. What is important to remember about Three-dimensional objects?

Answer: Three-dimensional objects is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q2. What is important to remember about Faces?

Answer: Faces is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about Edges?

Answer: Edges is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q4. What is important to remember about Vertices?

Answer: Vertices is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q5. What is important to remember about Nets?

Answer: Nets is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q6. What is important to remember about Surface area?

Answer: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area.

Q7. What is important to remember about Rectangular prisms?

Answer: Rectangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Triangular prisms?

Answer: Triangular prisms is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Cylinder parts?

Answer: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder parts.

Q10. What is important to remember about Cylinder net?

Answer: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Cylinder net.

Q11. What is important to remember about Lateral area of cylinder?

Answer: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Lateral area of cylinder.

Q12. What is important to remember about Surface area of cylinder?

Answer: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of cylinder.

Q13. What is important to remember about Square units?

Answer: Square units is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q14. What is important to remember about Packaging applications?

Answer: Packaging applications is an important Grade 7 idea in Surface Area of Prisms and Cylinders. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q15. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q16. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q17. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q18. When should you round?

Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.

Q19. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q20. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q21. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q22. What should you do if an answer seems unreasonable?

Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.

Q23. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.

Q24. Why are tables useful?

Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.

Q25. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer you obtained.

Q26. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.

Q27. How should you study this chapter?

Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.

Q28. When is a calculator useful?

Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.

Q29. Why compare more than one strategy?

Answer: Different strategies can make a problem easier and provide a way to verify the result.

Q30. What is a mathematical model?

Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.