Any ideas? This prob. is driving me crazy.
A cylindrical hole of radius x is bored through a sphere of radius R in such a way that the axis of the hole passes through the center of the sphere. Find the value of x that maximizes that complete surface area of the remaining solid. Hint: The area of a segment of height h on a sphere of radius R is 2(pi)Rh.
Any help will be appreciated. Thanks.