2008 AMC 12A Problem 8

Problem 8 of 25EasierGeometry

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

1?

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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.

Concepts: cube geometry · surface area · volume

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