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2003 AMC 10A 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 eight removed cubes have total volume 8⋅33=2168 \cdot 3^3 = 216 cubic centimeters. The original box has volume 15⋅10⋅8=120015 \cdot 10 \cdot 8 = 1200 cubic centimeters. The percent removed is 2161200⋅100%=18%.\dfrac{216}{1200} \cdot 100\% = 18\%. Thus, the correct answer is D.

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Concepts: volume · percentage · cube geometry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.