find the shape of the rectangular box of volume V for which the sum of the edge lengths is least.?

Question

that's all i have. go for it math/physics majors. i'm stumped.

Answer 1

cube root of V = length of a side...

so the box would be

V^1/3 x V^1/3 x V^1/3

Answer 2

This will be a cube, of side cube root of V. The proof can be done in two steps, each using simple calculus: first, show that the area is maximized by a square, and then that the volume is maximized by a cube. Or, you could probably do it with two variables and partial derivatives, but I haven't tried that.