2008 AMC 12A Problem 8

Below is the professionally curated solution for Problem 8 of the 2008 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 12A solutions, or check the answer key.

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Concepts:cube geometry surface area volume

Difficulty rating: 1380

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

$\sqrt{2}$

$2$

$2\sqrt{2}$

$4$

$8$

Solution:

The cube with volume $1$ has side $1$ and surface area $6.$ The larger cube has surface area $12,$ so if its side is $s,$ then $6s^2 = 12,$ giving $s = \sqrt{2}.$

Its volume is $(\sqrt{2})^3 = 2\sqrt{2}.$

Thus, C is the correct answer.

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