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 $6\sqrt[3]{V^2}.$