A six-sided rectangular box is to hold 1/2 cubic meter; what shape should the box be to minimize surface area?

A circle is an object which has the lowest surface area to volume ratio. So in this case, the shape should be like that of a circle but we cannot have a circle here because we want to form a 6 sided box. So the next thing closer to circle is a square. Hence the shape should be a square:

Answer:

square