How in general to set up your integral for computing volume

There are three main methods you can use: horizontal slices; vertical slices; or concentric shells. (But concentric shells work only if you have a volume of revolution, whereas you can always try the method of slicing. For a figure of revolution, the slices are perpendicular to the axis of revolution, so use vertical slices for a horizontal axis of revolution, and horizontal slices for a vertical axis of revolution.)

When you start a problem, you may not know which method is best. Just pick one and see what happens!

Concentric Shells