don't give up so easy. this problem is not as bad as you think.
this first equation is the total surface area of a cylinder ...
sub this into the volume formula for h ...
take the derivative w/r to r and set the result equal to zero ...
sub this value into the equation where h is in terms of r ... you should see that h = 2r ; the max volume for a fixed surface area occurs when the cylinder's side profile is a square.