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2003 AMC 12A Problem 3

Problem 3 of 25EasierAlgebraGeometry

A solid box is 1515 cm by 1010 cm by 88 cm. A new solid is formed by removing a cube 33 cm on a side from each corner of this box. What percent of the original volume is removed?

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Solution

The original volume is 15⋅10⋅8=1200.15 \cdot 10 \cdot 8 = 1200. Eight corner cubes are removed, each of volume 33=27,3^3 = 27, totaling 8⋅27=216.8 \cdot 27 = 216. The fraction removed is 2161200=0.18,\dfrac{216}{1200} = 0.18, which is 18%.18\%. Thus, the correct answer is D.

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Concepts: volume · percentage

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