So you are usingdisksnot "shells".

You have a wrong power:

the answer is supposed to be 648pi/5

The similarities between my answer and their answer makes me think my method is correct. See attached picture. I'm trying to get the shape to be like a. But I suspect my equation is giving me b. Especially because my answer is larger, and b looks like it would have a larger volume.

Can anyone clarify?