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1998 CEMC Gauss (Grade 7) Problems/Problem 14

Problem

A cube has a volume of $125 \text{cm}^3.$ What is the area of one face of the cube?


$\text{(A)}\ 20 \text{cm}^2 \qquad \text{(B)}\ 25 \text{cm}^2 \qquad \text{(C)}\ 41 \dfrac{2}{3} \text{cm}^2 \qquad \text{(D)}\ 5 \text{cm}^2 \qquad \text{(E)}\ 75 \text{cm}^2$

Solution

The side length of the cube is $\sqrt[3]{125} = 5$ cm, so the area of one face is $5^2 = 25 \text{cm}^2.$

The answer is $\text{(B)}.$

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