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  1. AP Maths
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Volumes of Revolution

Emily Davis

Emily Davis

5 min read

Next Topic - Disc Method Around the y-Axis

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Study Guide Overview

This study guide covers calculating the volume of revolution around the x-axis using the disc method. It explains the formula V = π∫ab[f(x)]² dx and provides a worked example, practice questions, exam tips, and a glossary of key terms like solid of revolution, region, and definite integral.

#Volume with Disc Method Revolving Around the x-axis

#Table of Contents

  1. Introduction to Volume of Revolution
  2. Using the Disc Method
  3. Exam Tips
  4. Worked Example
  5. Practice Questions
  6. Summary and Key Takeaways
  7. Glossary

#Introduction to Volume of Revolution

#What is a Volume of Revolution Around the x-axis?

A solid of revolution is formed when an area bounded by a function y=f(x)y=f(x)y=f(x) (and other boundary equations) is rotated 2\pi radians (360°) around the xxx-axis. The volume of revolution is the volume of this solid.

Be careful – the 'front' and 'back' of this solid are flat because they were created from straight (vertical) lines. 3D sketches can be misleading.

#Using the Disc Method

#How to Calculate a Volume of Revolution Around the x-axis?

For a continuous function fff, if the region bounded by:

  • the curve y=f(x)y=f(x)y=f(x) and the xxx-axis
  • between x=ax=ax=a and x=bx=bx=b

is rotated 2\pi radians (360°) around the xxx-axis, then the volume of revolution is:

V = \pi \int_...
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Question 1 of 8

What is a solid of revolution? 🤔

A 2D shape rotated around an axis

A 3D shape formed by rotating an area around an axis

A 3D shape formed by shifting an area

Any 3D shape with circular cross-sections