




We slice a sphere of radius R by a cylinder of height h and radius R._{ }
Minimize the surface area of the cylindrical sides if the sphere is fixed.
Condition:
Area of the cylindrical sides: A= 2prh
We minimize
Compure partial derivatives
The critcal condition becomes
But here it is the condition for maximum cylindric area; the minimum area, zero, occurs at h = 0, r = R and at r = 0, h = 2R.