# What is the ratio of surface area to volume for a cube with a volume of 64 cubic inches?

Jul 4, 2015

#### Explanation:

The formula for the volume of a cube is

$V = {a}^{3}$, where $a$ is the length of a side.

a = root3V = root3("64 in"^3) = "4 in"

Each face of the cube is a square.

A = a^2 = ("4 in")^2 = "16 in"^2

A cube has 6 faces, so the surface area of the cube is given by

${\text{SA" = 6 cancel("faces") × ("16 in"^2)/(1 cancel("face")) = "96 in}}^{2}$

$\text{SA"/"V} = \frac{96}{64} = \frac{1.5}{1}$