Question

If the radius of a cylinder is increased by 10% and height remains unchanged, then what is the percentage of increase in volume ?

• A. 10%
• B. 20%
• C. 11%
• D. 21%

Answer 1

Answer:

D. 21%

$v=\pi r^2h$

$r_1=original radius = 1$

$r_2=increased radius=1.1 \times r_1$

$v_1=\pi r_1^2h$

$v_2=\pi (1.1 \times r_1)^2h$

% increase =$\frac{v_2-v_1}{v_1}\times 100$

$=\frac{(\pi(1.1\times r_1)^2h)-(\pi r_1^2h)}{\pi r_1^2h}\times 100$

$=\frac{\pi r_1^2h(1.1^2-1)}{\pi r_1^2h}\times 100$

$=1.21-1 \times 100$

$=21$