The surface area of a cube is $24 \mathrm{~cm}^{2}$. The volume of this cube is
(A) $4 \mathrm{~cm}^{3}$
(B) $24 \mathrm{~cm}^{3}$
(C) $8 \mathrm{~cm}^{3}$
(D) $27 \mathrm{~cm}^{3}$
(E) $64 \mathrm{~cm}^{3}$
The surface area of a cube is $24 \mathrm{~cm}^{2}$. The volume of this cube is
(A) $4 \mathrm{~cm}^{3}$
(B) $24 \mathrm{~cm}^{3}$
(C) $8 \mathrm{~cm}^{3}$
(D) $27 \mathrm{~cm}^{3}$
(E) $64 \mathrm{~cm}^{3}$

## Solution

A cube has six square faces of equal area, so each of these faces has area $\frac{1}{6} \times 24 \mathrm{~cm}^{2}=4 \mathrm{~cm}^{2}$. This tells us that the side length of the cube must be $2 \mathrm{~cm}$. The volume of the cube is $2 \mathrm{~cm} \times 2 \mathrm{~cm} \times 2 \mathrm{~cm}=8 \mathrm{~cm}^{3}$.