### 8.3: Volume of Solids of Revolution

When we are presented with a solid that was produced by rotating a curve around an axis, there are two sensible ways to take that solid apart: slice it thinly perpendicularly to the axis, into disks (or washers, if the solid had a hole in the middle), or peel layers from around the outside like the paper wrapper of a crayon. The latter method is known as the shell method and produces thin cylinders. In both cases, we find the area of the thin segments and add them up to find the volume; as usual, when we have infinitely many pieces, this addition is really integration.

### 8.3.1: Disks and Washers

Read Section 6.2 (pages 308 through 318).

Watch this video. Dr. Jerison elaborates on some tangential material for a few minutes in the middle, but returns to the essential material very quickly.

Click on the "Index" for Book II. Scroll down to "2. Applications of Integration," and click button 119 (Solid of Revolution - Washers). Work on problems 1-12. If at any time a problem set seems too easy for you, feel free to move on.

### 8.3.2: Cylindrical Shells

Click on the "Index" for Book II. Scroll down to "2. Applications of Integration," and click button 120 (Solid of Revolution - Shells). Work on problems 5-17. If at any time a problem set seems too easy for you, feel free to move on.