Using the shell method, set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.
y = x3 bounded by y = 8, and x = 0.
volume of a solid revolved around x-axis using the shell method.
The Attempt at a Solution
I have to find the height h(y) of some arbitrary shell and the average radius p(y) of all shells multiply them together and then integrate them, which I am fairly confident I can do so I am not going to worry about that at this time. For my height, h(y), I have a distance of "y" and I understand that. But the average radius p(y) is what I do not understand, the answer says that they are just multiplying the height by x(y), y1/3, which they do because they are integrating wrt y. But geometrically, I would have thought the average radius would be (8 - y1/3).