I think I've figured out how to start the problem. Please, someone, let me know if this is right.
I would look at the surface area of each slice, from 0 to r. Since each surface area is equal to the distance of how far that square is from r, we can call that point x, and integrate like this:
, from 0 to r.
Is this right? If it is, how to I get x in terms of r?