A copper water tank in the form of a rectangular parallelopiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?

W.E. Berely, * Problems in Differential Calculus *, 1895

The answer is: a:a+1 if tank is open, 2a:a+1 if it is closed.