2003 AMC 10A Problem 3

Problem 3 of 25EasierGeometry Arithmetic

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?

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Solution

The eight removed cubes have total volume

8 \cdot 3^3 = 216

cubic centimeters. The original box has volume

15 \cdot 10 \cdot 8 = 1200

cubic centimeters. The percent removed is

\dfrac{216}{1200} \cdot 100\% = 18\%.

Thus, the correct answer is D.

Tagged: volume · percentage · cube geometry