Question

A cylinder (r = 4cm, h = 10 cm) is bored through by a hole (r = 2 cm, full height). What percentage of original volume is removed?

• A. 25%
• B. 50%
• C. 75%
• D. 37.5%

Answer 1

Answer:

A. 25%

Step 1: Original volume of cylinder

$V_{\text{original}} = \pi r^2 h = \pi \times 4^2 \times 10 = 160\pi$

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Step 2: Volume removed (hole)

$V_{\text{removed}} = \pi \times 2^2 \times 10 = 40\pi$

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Step 3: Percentage removed

$\frac{40\pi}{160\pi} \times 100 = \frac{1}{4} \times 100 = 25\%$

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Final Answer:

$\boxed{25\%}$