If the surface area of a cube is 54 , what is its volume?
(A) 36
(B) 9
(C) $\frac{81 \sqrt{3}}{8}$
(D) 27
(E) $162 \sqrt{6}$
If the surface area of a cube is 54 , what is its volume?
(A) 36
(B) 9
(C) $\frac{81 \sqrt{3}}{8}$
(D) 27
(E) $162 \sqrt{6}$

## Solution

Let each edge of the cube have length $x$. Then each face of the cube has area $x^{2}$. Since a cube has six faces, the surface area of the cube is $6 x^{2}$.

We know $6 x^{2}=54$

$$
\begin{array}{r}
x^{2}=9 \\
x=3
\end{array}
$$

Since each edge of the cube has length 3 , the volume of the cube is $3^{3}=27$.

ANSWER: (D)