This may seem like a very simple problem.
If you are given the surface area of a sphere how do you find the radius and height. For example if the surface area of a cylinder including both ends in 60^2 how would you find the height and radius.
Any help would be appreciated
and from above you can solve for h to get
If you put this into the volume formula you get
Now you need to maximize the volume.
Since this is a cubic if you want an analytic solution you will need to use calculus and the derivative. If you do not know calculus plot the function on a graphing device and find the maximum volume.