1959 AHSME Problems/Problem 1

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Problem 1

Each edge of a cube is increased by $50$%. The percent of increase of the surface area of the cube is: $\textbf{(A)}\ 50 \qquad\textbf{(B)}\ 125\qquad\textbf{(C)}\ 150\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 750$

Solution

Note that increasing the length of each edge by $50$% with result in a cube that is similar to the original cube with scale factor $1.5$. Therefore, the surface area will increase by a factor of $1.5^2$, or $2.25$. Converting this back into a percent, the percent increase will be $125$%. Therefore, the answer is $\boxed{\textbf{B}}$.

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