How can I show that for a given volume, a convex polyhedron will have a smaller surface area than a nonconvex polyhedron?

How can I show that for a given volume, a convex orthogonal polyhedron will have a smaller surface area than a nonconvex orthogonal polyhedron?

If this is not possible to show, can it be shown that a cube will have a smaller surface area than any other orthogonal polyhedron, convex or nonconvex, of the same volume? How?