Question

An open box has a square base and a volume of 32 in3. find the dimensions of the box, assuming a minimum amount of material is used in its construction.

Answer 1

For minimum material to be used, the box should be a cube. Hence the volume will be as follows:
let the dimensions be x in by x in by x in
thus
V=x×x×x
32=x³ in³
hence:
x=∛32
x=2∛2 inches
Hence the length=width=height=2∛2