A cube has a surface area of $54 \mathrm{~cm}^{2}$. The volume of the cube, in $\mathrm{cm}^{3}$, is
(A) 81
(B) 343
(C) 18
(D) 27
(E) 729
Let $s$ be the side length of the cube.

The surface area of a cube is made up of 6 identical squares.

Since the surface area is $54 \mathrm{~cm}^{2}$, then each of the 6 squares has area $(54 \div 6) \mathrm{cm}^{2}=9 \mathrm{~cm}^{2}$.

The area of a square with side length $s$ is $s^{2}$, so $s^{2}=9$ or $s=\sqrt{9}=3 \mathrm{~cm}$.

The volume of a cube is given by the product of its length, width and height, which are all equal to $s, 3 \mathrm{~cm}$.

Thus the volume of the cube with surface area $54 \mathrm{~cm}^{2}$ is $3 \times 3 \times 3=27 \mathrm{~cm}^{3}$.

ANSWER: (D)

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