2008 AMC 12A Problems/Problem 8

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Problem

What is the volume of a cube whose surface area is twice that of a cube with volume 1?

$\textbf{(A)} \sqrt{2} \qquad \textbf{(B)} 2  \qquad \textbf{(C)} 2\sqrt{2}  \qquad \textbf{(D)}  4  \qquad \textbf{(E)}  8$

Solution

A cube with volume $1$ has a side of length $\sqrt[3]{1}=1$ and thus a surface area of $6 \cdot 1^2=6$.

A cube whose surface area is $6\cdot2=12$ has a side of length $\sqrt{\frac{12}{6}}=\sqrt{2}$ and a volume of $(\sqrt{2})^3 = 2\sqrt{2} \Rightarrow C$.

See Also

2008 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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All AMC 12 Problems and Solutions