Mathematics Advanced Year 11 - Module 3 - Lesson 13

Volumes of Solids of Revolution

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

Spin a curve around an axis and it traces out a three-dimensional solid — a vase, a rocket nose cone, or a wine glass. By slicing that solid into infinitely thin disks and adding up their volumes, we can find the exact volume of almost any rotational shape. This is the power of volumes of solids of revolution.

  • The disk method formula for rotation about the $x$-axis and $y$-axis
  • How revolving a curve generates a three-dimensional solid

2. Success Criteria

By the end, you should be able to:

  • The disk method formula for rotation about the $x$-axis and $y$-axis
  • The washer method for regions between two curves
  • How to identify the radius function for a given solid

3. Key Terms

Thisthe power of volumes of solids of revolution
Each infinitesimally thin slicea disk with volume $\pi r^2 \cdot \text{thickness}$
Point of Inflectionthe reverse of differentiation, but includes an arbitrary constant (+C) for indefinite integrals
each sliceapproximately a circular disk with:
the region being rotatedbounded by two curves, the cross-section is a
volume of each washerthe volume of the outer disk minus the volume of the inner disk:

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The disk method formula for rotation about the $x$-axis and $y$-axis". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "The washer method for regions between two curves". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Volumes of Solids of Revolution: "How to identify the radius function for a given solid".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Volumes of Solids of Revolution but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Volumes of Solids of Revolution?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Volumes of Solids of Revolution?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The disk method formula for rotation about the $x$-axis and $y$-axis

Band 32 marks
Success criterion 2

Prove that you can: The washer method for regions between two curves

Band 43 marks
Success criterion 3

Prove that you can: How to identify the radius function for a given solid

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 3 - Lesson 13

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Mathematics Advanced Year 11 - Module 3 - Lesson 13

Volumes of Solids of Revolution

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

Spin a curve around an axis and it traces out a three-dimensional solid — a vase, a rocket nose cone, or a wine glass. By slicing that solid into infinitely thin disks and adding up their volumes, we can find the exact volume of almost any rotational shape. This is the power of volumes of solids of revolution.

  • The disk method formula for rotation about the $x$-axis and $y$-axis
  • How revolving a curve generates a three-dimensional solid

2. Success Criteria

By the end, you should be able to:

  • The disk method formula for rotation about the $x$-axis and $y$-axis
  • The washer method for regions between two curves
  • How to identify the radius function for a given solid

3. Key Terms

Thisthe power of volumes of solids of revolution
Each infinitesimally thin slicea disk with volume $\pi r^2 \cdot \text{thickness}$
Point of Inflectionthe reverse of differentiation, but includes an arbitrary constant (+C) for indefinite integrals
each sliceapproximately a circular disk with:
the region being rotatedbounded by two curves, the cross-section is a
volume of each washerthe volume of the outer disk minus the volume of the inner disk:

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The disk method formula for rotation about the $x$-axis and $y$-axis". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "The washer method for regions between two curves". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Volumes of Solids of Revolution: "How to identify the radius function for a given solid".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Volumes of Solids of Revolution but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Volumes of Solids of Revolution?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Volumes of Solids of Revolution?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The disk method formula for rotation about the $x$-axis and $y$-axis

Band 32 marks
Success criterion 2

Prove that you can: The washer method for regions between two curves

Band 43 marks
Success criterion 3

Prove that you can: How to identify the radius function for a given solid

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 3 - Lesson 13

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Mathematics Advanced Year 11 - Module 3 - Lesson 13

Volumes of Solids of Revolution

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

Spin a curve around an axis and it traces out a three-dimensional solid — a vase, a rocket nose cone, or a wine glass. By slicing that solid into infinitely thin disks and adding up their volumes, we can find the exact volume of almost any rotational shape. This is the power of volumes of solids of revolution.

  • The disk method formula for rotation about the $x$-axis and $y$-axis
  • How revolving a curve generates a three-dimensional solid

2. Success Criteria

By the end, you should be able to:

  • The disk method formula for rotation about the $x$-axis and $y$-axis
  • The washer method for regions between two curves
  • How to identify the radius function for a given solid

3. Key Terms

Thisthe power of volumes of solids of revolution
Each infinitesimally thin slicea disk with volume $\pi r^2 \cdot \text{thickness}$
Point of Inflectionthe reverse of differentiation, but includes an arbitrary constant (+C) for indefinite integrals
each sliceapproximately a circular disk with:
the region being rotatedbounded by two curves, the cross-section is a
volume of each washerthe volume of the outer disk minus the volume of the inner disk:

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The disk method formula for rotation about the $x$-axis and $y$-axis". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "The washer method for regions between two curves". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Volumes of Solids of Revolution: "How to identify the radius function for a given solid".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Volumes of Solids of Revolution but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Volumes of Solids of Revolution?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Volumes of Solids of Revolution?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The disk method formula for rotation about the $x$-axis and $y$-axis

Band 32 marks
Success criterion 2

Prove that you can: The washer method for regions between two curves

Band 43 marks
Success criterion 3

Prove that you can: How to identify the radius function for a given solid

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 3 - Lesson 13