2008 AMC 12A Problem 8

Attempt Problem 8 of the 2008 AMC 12A below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

A cube with volume

1

has surface area

6

If the larger cube has side

s,

then

6s^2 = 12

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.

Problem 8 in other years