It can be shown that the surface area of a cylinder is minimum when height=diameter.

Calculus is one of the easiest to do this with. It's not too bad.

Here is a general case, then you can use whatever V you wish.

Assuming it has a top and bottom:

........[1]

.......[2]

Solve [2] for h and sub into [1]:

........[3]

Set this to 0 and solve for r and we get

Sub into [3] and find

See?. h is twice r just as was stated in the beginning.