Exercises choosing a method for computing volume.

The region in the plane bounded by and the -axis for is rotated about the -axis. The volume of the resulting solid of revolution is (Hints won’t be revealed until after you choose a response.)
The region in the plane bounded on the right by the curve , on the left by the curve , and on the bottom by is revolved around the -axis. Compute the volume of the resulting solid.
Compute the volume of the solid of revolution obtained by rotating the region between , , and around the -axis.

The region between the graph of and the -axis is rotated around the line . What is the volume of the resulting solid?

Find the volume obtained by rotating the region between the graph and the -axis for about the -axis.

Sample Exam Questions

Calculate the volume of the solid obtained by rotating the area between the graphs of and the -axis for around the -axis.

Let be a continuous function that satisfies and for . For every , when the region between the graph of , the -axis, and the line is rotated around the -axis, the volume of the resulting solid is . What is ? (Hints will not be revealed until after you choose a response.)

Find the volume of the solid generated by revolving the region bounded above by and bounded below by for about the -axis.

none of these