Question

A solid cylinder radius 5 cm is drilled by four cylindrical holes each radius 1 cm length equal to the full height. Volume removed is approximately what percent?

• A. 16%
• B. 20%
• C. 25%
• D. 8%

Answer 1

Answer:

A. 16%

Let the cylinder have height (h).

Original cylinder volume:
$V_{\text{orig}} = \pi r^2 h = \pi (5^2)h = 25\pi h$

Volume removed by 4 cylindrical holes:
Each hole:
$\pi (1^2)h = \pi h$

Four holes:
$V_{\text{removed}} = 4\pi h$

Percentage removed:
$\frac{4\pi h}{25\pi h} \times 100 = \frac{4}{25} \times 100 = 16\%$

Answer: $(\boxed{16\%})$