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Chapter 47: Volume of Prisms and Cylinders

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

47.1 Meaning of volume

The mean is the sum of all values divided by the number of values. In this section, the focus is Meaning of volume.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Meaning of volume. Show the important steps, include units when needed, and explain how you checked the answer.

47.2 Cubic units

Cubic units is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Cubic units. Show the important steps, include units when needed, and explain how you checked the answer.

47.3 Rectangular-prism volume

Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Rectangular-prism volume.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Rectangular-prism volume. Show the important steps, include units when needed, and explain how you checked the answer.

47.4 Triangular-prism volume

Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Triangular-prism volume.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Triangular-prism volume. Show the important steps, include units when needed, and explain how you checked the answer.

47.5 Cylinder volume

Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Cylinder volume.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Cylinder volume. Show the important steps, include units when needed, and explain how you checked the answer.

47.6 V = πr²h

V = πr²h is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: V = πr²h: Explain V = πr²h in one simple sentence.

  1. Look at the words in “V = πr²h”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: V = πr²h is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: V = πr²h: A student says, “I can use V = πr²h without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: V = πr²h: What is the first step when solving a problem about V = πr²h?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: V = πr²h: After solving a V = πr²h problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: V = πr²h: Give one way V = πr²h could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: V = πr²h can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: V = πr²h: Which representation could help explain V = πr²h: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: V = πr²h: A student gets an answer for V = πr²h but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: V = πr²h: Why can estimation help before a detailed V = πr²h calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: V = πr²h: How can you test whether your rule for V = πr²h works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: V = πr²h: How would you teach V = πr²h to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving V = πr²h. Show the important steps, include units when needed, and explain how you checked the answer.

47.7 Finding missing height

Finding missing height is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Finding missing height: Explain Finding missing height in one simple sentence.

  1. Look at the words in “Finding missing height”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: Finding missing height is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Finding missing height: A student says, “I can use Finding missing height without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: Finding missing height: What is the first step when solving a problem about Finding missing height?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: Finding missing height: After solving a Finding missing height problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: Finding missing height: Give one way Finding missing height could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: Finding missing height can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Finding missing height: Which representation could help explain Finding missing height: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: Finding missing height: A student gets an answer for Finding missing height but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: Finding missing height: Why can estimation help before a detailed Finding missing height calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: Finding missing height: How can you test whether your rule for Finding missing height works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: Finding missing height: How would you teach Finding missing height to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving Finding missing height. Show the important steps, include units when needed, and explain how you checked the answer.

47.8 Finding missing base dimensions

Finding missing base dimensions is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Finding missing base dimensions: Explain Finding missing base dimensions in one simple sentence.

  1. Look at the words in “Finding missing base dimensions”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: Finding missing base dimensions is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Finding missing base dimensions: A student says, “I can use Finding missing base dimensions without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: Finding missing base dimensions: What is the first step when solving a problem about Finding missing base dimensions?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: Finding missing base dimensions: After solving a Finding missing base dimensions problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: Finding missing base dimensions: Give one way Finding missing base dimensions could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: Finding missing base dimensions can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Finding missing base dimensions: Which representation could help explain Finding missing base dimensions: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: Finding missing base dimensions: A student gets an answer for Finding missing base dimensions but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: Finding missing base dimensions: Why can estimation help before a detailed Finding missing base dimensions calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: Finding missing base dimensions: How can you test whether your rule for Finding missing base dimensions works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: Finding missing base dimensions: How would you teach Finding missing base dimensions to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving Finding missing base dimensions. Show the important steps, include units when needed, and explain how you checked the answer.

47.9 Comparing volumes

Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Comparing volumes.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Comparing volumes. Show the important steps, include units when needed, and explain how you checked the answer.

47.10 Capacity connections

Capacity connections is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Capacity connections. Show the important steps, include units when needed, and explain how you checked the answer.

47.11 Millilitres and cubic centimetres

Millilitres and cubic centimetres is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Millilitres and cubic centimetres. Show the important steps, include units when needed, and explain how you checked the answer.

47.12 Litres and cubic decimetres

Litres and cubic decimetres is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Litres and cubic decimetres. Show the important steps, include units when needed, and explain how you checked the answer.

47.13 Real-life volume problems

Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Real-life volume problems.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Use V = lwh.
  2. V = 4×2×3.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 24 cm³

Worked Example 2

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

  1. Use V = lwh.
  2. V = 5×3×4.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 60 cm³

Worked Example 3

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

  1. Use V = lwh.
  2. V = 6×4×5.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 120 cm³

Worked Example 4

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

  1. Use V = lwh.
  2. V = 7×5×6.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 210 cm³

Worked Example 5

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

  1. Use V = lwh.
  2. V = 8×6×7.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 336 cm³

Worked Example 6

Problem: Find the volume of a rectangular prism 9 cm × 7 cm × 8 cm.

  1. Use V = lwh.
  2. V = 9×7×8.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 504 cm³

Worked Example 7

Problem: Find the volume of a rectangular prism 10 cm × 8 cm × 9 cm.

  1. Use V = lwh.
  2. V = 10×8×9.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 720 cm³

Worked Example 8

Problem: Find the volume of a rectangular prism 11 cm × 9 cm × 10 cm.

  1. Use V = lwh.
  2. V = 11×9×10.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 990 cm³

Worked Example 9

Problem: Find the volume of a rectangular prism 12 cm × 10 cm × 11 cm.

  1. Use V = lwh.
  2. V = 12×10×11.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1320 cm³

Worked Example 10

Problem: Find the volume of a rectangular prism 13 cm × 11 cm × 12 cm.

  1. Use V = lwh.
  2. V = 13×11×12.

Very beginner explanation: Volume measures 3D space, so cubic units are used.

Answer: 1716 cm³

Practice exercise

Create one new Grade 8 problem involving Real-life volume problems. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 47 Review Questions and Answers

Q1. What is important to remember about Meaning of volume?

Answer: The mean is the sum of all values divided by the number of values. In this section, the focus is Meaning of volume.

Q2. What is important to remember about Cubic units?

Answer: Cubic units is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about Rectangular-prism volume?

Answer: Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Rectangular-prism volume.

Q4. What is important to remember about Triangular-prism volume?

Answer: Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Triangular-prism volume.

Q5. What is important to remember about Cylinder volume?

Answer: Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Cylinder volume.

Q6. What is important to remember about V = πr²h?

Answer: V = πr²h is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Finding missing height?

Answer: Finding missing height is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Finding missing base dimensions?

Answer: Finding missing base dimensions is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Comparing volumes?

Answer: Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Comparing volumes.

Q10. What is important to remember about Capacity connections?

Answer: Capacity connections is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q11. What is important to remember about Millilitres and cubic centimetres?

Answer: Millilitres and cubic centimetres is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Litres and cubic decimetres?

Answer: Litres and cubic decimetres is an important Grade 8 concept in Volume of Prisms and Cylinders. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Real-life volume problems?

Answer: Volume measures the three-dimensional space inside an object and uses cubic units. In this section, the focus is Real-life volume problems.

Q14. Why should you show your steps?

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

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

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

Q17. When should you round?

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

Q18. How can you check an answer?

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

Q19. What should you identify first in a word problem?

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

Q20. What makes a final answer complete?

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

Q21. What should you do if an answer seems unreasonable?

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

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

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

Q24. Why should you explain your reasoning?

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

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

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

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.