2003 AMC 12A Problem 3

Attempt Problem 3 of the 2003 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 2003 AMC 12A solutions, or check the answer key.

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A solid box is $15$ cm by $10$ cm by $8$ cm. A new solid is formed by removing a cube $3$ cm on a side from each corner of this box. What percent of the original volume is removed?

$4.5$

$9$

$12$

$18$

$24$

Answer: D

Concepts:volume percentage

Difficulty rating: 1130

Solution:

The original volume is $15 \cdot 10 \cdot 8 = 1200.$

Eight corner cubes are removed, each of volume $3^3 = 27,$ totaling $8 \cdot 27 = 216.$

The fraction removed is $\dfrac{216}{1200} = 0.18,$ which is $18\%.$

Thus, the correct answer is D.

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