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A solid cylinder of radius 6 cm has five cylindrical holes of radius 1.5 cm each drilled throughout its length. Approximately what percent of the volume is removed?

1. 25.25%
2. 36.60%
3. 42.75%
4. 31.25%

Correct answer: 31.25%

Solution

The removed volume is proportional to the total area of the five holes. Main cylinder area = \(\pi\times 6^2 = 36\pi\). Area of one hole = \(\pi\times 1.5^2 = 2.25\pi\), so five holes remove \(11.25\pi\). Percentage removed = \(\frac{11.25}{36}\times 100 = 31.25\%\).

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