Final Thoughts:

Here is a list of items to keep in mind when selecting the shell method:

1. Your representative rectangle is parallel to the axis of revolution.

2. Identify the radius carefully.

3. Take time to always sketch an accurate drawing and include the 180-degree shadow.

4. Your limits of integration run opposite the axis of revolution.

5. Remember to inclue the "2" in your formula which is part of the circumference of a circle formula!

6. Never rule out that disks/washers might be easier. Look at both possibilities.