Question

A rectangular prism has dimensions 8 inches by 2 inches by 32 inches. if a cube has the same volume as the prism, what is the surface area of the cube, in square inches?

Answer 1

The formula for volume of a rectangular prism is V = l × w × h, but a cube is
V = a³

We know the volume of the cube because it is the same as the prism, and we know the prism because of V = l × w × h.

V = 8 × 2 × 32... V = 512

So the cube's volume is 512 as well

So... 512 = a³
∛512 = a
a = 8

a is one side of the cube, a² is one face. A cube has 6 faces similar to a die with six numbers. So 6 × a² is the surface area. 384 is your answer.