2016 AMC 10A Problems/Problem 5

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Problem

A rectangular box has integer side lengths in the ratio $1: 3: 4$. Which of the following could be the volume of the box?

$\textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 144$

Solution

Let the smallest side length be $x$. Then the volume is $x \cdot 3x \cdot 4x =12x^3$. If $x=2$, then $12x^3 = 96 \implies \boxed{\textbf{(D) } 96.}$

See Also

2016 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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All AMC 10 Problems and Solutions

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