It looks like wherever you found the answer used the method of shells. The formula for shell integration is (when the axis of revolution is the y-axis).
According to the formula for shell integration, the volume V of the solid is given by:
The region bounded by and is revolved about the y-axis. Find the volume of the resulting solid.
I know that the answer is , however I am not sure how to get there. I drew a picture, and I can't tell if I'm supposed to approximate with disks or shells...or approach it a different way. Any insight offered is appreciated. Thanks in advance.