Minimising the surface area of a Cuboid with a different length, width, and height. I've been trying to minimise the surface of a Cuboid, with a different length, width, and height, but I haven't been able to do so, considering that there is more than 2 variables. The constraint being the volume of the cuboid. Considering the following equations: S.A of cuboid = 2(wl+hl+hw) V = whl Any help would be appreciated. Thanks!

If it means that the volum $V$ is given we can make the following.

By AM-GM $$2(wl+hl+hw)\geq2\cdot3\sqrt[3]{wl\cdot hl\cdot hw}=6\sqrt[3]{w^2l^2h^2}=6\sqrt[3]{V^2}.$$

The equality occurs for $w=l=h,$ which is impossible by the given.

Id est, the minimal value does not exist, but the infimum is $6\sqrt[3]{V^2}.$