1. AP Calculus Honors Ms. Olifer
Volumes of Revolution
AP Calculus Honors
Ms. Olifer

2. Volumes of Revolution
A solid of revolution is a solid obtained by rotating a region in the plane about an axis.
For example, the right circular cone and the sphere are solids of revolution.

4. Volume of a Solid of Revolution: Disk Method

5. Example 1

6. Volume of the region between 2 curves
The cross section is a washer of outer radius R = f(x) and inner radius r=g(x). The area of this washer is

7. Volume of the region between 2 curves

8. Example 2

9. Example 3

10. Solution

11. Solution (continued)