A rectangular prism has a volume of 60 in³. what is the least possible surface area of the prism?

and

A rectangular prism has a volume of 24 m³. What is the least possible surface area of the prism?

The rectangular prism that has the least surfacea area for a given volume is a cube. If the volume is given by V, the side length (s) will be

... V = s³

... ∛V = s

Then the surface area will be

... A = 6*s²

... A = 6 (∛V) ²

... A = 6*V^ (2/3)

a) For a cuboid with volume 60 in³, the least possible surface area is

... A = 6 * (60 in³) ^ (2/3) ≈ 91.957 in²

b) For a cuboid with volume 24 m³, the least possible surface area is

... A = 6 * (24 m³) ^ (2/3) ≈ 49.922 m²