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Lesson Packs · Grade 12 · Mathematics

Volumes of Solids of Revolution

Students find the volumes of solids formed by rotating a region about the x-axis with the disk and washer methods, derive the volumes of a cone, a sphere and a paraboloid, and find volumes when a region is rotated about the y-axis.

Unit 4 · Lesson 17 · Integration

Preview

Volumes of Solids of Revolution — Slide 1
  • Volumes of Solids of Revolution — Slide 4
    Slide 4
  • Volumes of Solids of Revolution — Slide 10
    Slide 10
  • Volumes of Solids of Revolution — Slide 17
    Slide 17
  • Volumes of Solids of Revolution — Slide 18
    Slide 18
  • Volumes of Solids of Revolution — Worksheet, page 1
    Worksheet, page 1
  • Volumes of Solids of Revolution — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Explain how rotating a region about the x-axis creates a solid made of thin disks, and use V = ∫ₐᵇ πy² dx.
  • Use the washer method for solids with a hole, and derive the volumes of a cone and a sphere.
  • Find the volume of a solid formed by rotating a region about the y-axis, using V = ∫_(c)ᵈ πx² dy.

What's inside

  • 42 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 11 worksheet questions (34 marks) with step-by-step solutions
  • Printable worksheet (4 pages) and a teacher answer key
  • Fully editable in PowerPoint, Google Slides, Keynote and Word

More lessons in this unit

Questions teachers ask

Can I edit the files?

Yes. The PowerPoint and the Word worksheet are fully editable, so you can change examples, add questions or adapt the design for your class.

How do I use the worksheet slides?

After the teaching slides, each worksheet question appears on its own slide. Let students try it first, then show the next slide and work through the solution together.

Is there an answer key?

Yes. The Word file ends with a teacher answer key that has the answer and a worked solution for every question. It is also included as a separate PDF.

Which languages are available?

Every Lesson Pack is made in 18 languages: English, Simplified Chinese, Hindi, Spanish, Arabic, French, Bengali, Portuguese, Indonesian, Urdu, Vietnamese, Albanian, Italian, German, Turkish, Malay, Greek and Traditional Chinese (Hong Kong).

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