Volumes of Revolution

Emily Davis
6 min read
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Study Guide Overview
This study guide covers the disc method for finding volumes of solids of revolution. It focuses on rotations around axes parallel to the x-axis and y-axis. Key topics include setting up integrals using or , rewriting equations, and applying the method through worked examples. Practice questions, a glossary, and exam strategies are also provided.
#Volume with Disc Method Revolving Around Other Axes
#Table of Contents
- Introduction
- Volume of Revolution Around Axes Parallel to the x-axis
- Volume of Revolution Around Axes Parallel to the y-axis
- Practice Questions
- Glossary
- Summary and Key Takeaways
- Exam Strategy
#Introduction
The disc method is a powerful technique used in calculus to find the volume of a solid of revolution. When a region in the plane is revolved around a line that is parallel to either the x-axis or the y-axis, we can use the disc method to calculate the volume of the resulting solid.
#Volume of Revolution Around Axes Parallel to the x-axis
#Key Concepts
- For a continuous function , if the region bounded by:
- The curve and the line
- Between and
- is rotated around the line , then the volume of revolution is:
- Thinking of this as an accumulation of change:
- is the volume of a disc with:
- Circular cross section of radius
- Length
- ...
- is the volume of a disc with:

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