I had this hw question (I solved to completion) LetV be the volume of the solid obtained by rotating about they-axis the region bounded by the following curves.

FindV by cylindrical shell

I understand that the formula is integral 2pi(radius)(height)d(x or y)

To find the height, you do the "top of the shell"-"the bottom of the shell"

in this problem, it was sqrtx-x^2

My question is, why is the radius = to x?

Is it that all cylindrical shell problems that the radius=x? My professor showed us numerous examples and they all had radius=x

I made a note in my book that radius could be the line it touches in a graph

(we had a problem that said to find volume revolving y axis by y=x^2 y=x ... Anyway, after making the cylindrical shell, the radius line we drew hit the line y=x so I figured maybe this was a rule??)

I am confused how to find the radius. Any help appreciated! Thank you.