Can someone help me with a proof for symmetry in trying to maximize the volume of a box, or a general form would be even better. The box is in its most simple form V=xyz, with a limited amount of surface area. First the eqeuation must be solved in one dimension to reduce it to two variables then partial derivation may be used to solve the equation. My assumption is that the volume would be maximized, (IF you have a limited surface area to work with) if you let the sides be square; i.e. x=y. I know this may seem obvious but is there any general mathematicalproof for this?