Volume of a Solid of Revolution Washer Method 

This lesson teaches you how to use the washer method for finding the volume of a solid of revolution.

Summary

The video will show you how to find volume when a region is bounded by two functions and rotated about the x-axis or y-axis, creating a solid with a hole in the middle. The lesson emphasizes identifying the outer radius and inner radius, setting up the correct integral, and avoiding common mistakes when squaring expressions. Examples include both hand-calculated problems and AP-style setups using Desmos, helping you understand how to show correct work on free-response questions.

Key Takeaways

• The washer method is used when a solid of revolution has a hole.

• Each cross section is a circle with a hole, called a washer.

• The area of a washer is π(R² − r²). 

• Do not square the difference of the radii.

• The volume formula is V = π∫ (R² − r²) dx (or dy).

• The outer radius comes from the top function; the inner radius comes from the bottom function.

• Limits of integration come from where the bounding functions intersect.

• On AP free-response questions, correct setup is often more important than evaluation.

Transcript

All right everyone, Mr. Antonucci here. We’re on part three of Section 8.3, and this time we’re going to talk about the washer method.