A solid cylinder is reduced in radius by 20% and increased in height by 50%. What net percentage change occurs in its volume?

Solution:

Volume of a cylinder $V = \pi r^2 h$.

Radius is reduced by $20%$, so new radius
$= 0.8r$.

Height is increased by $50%$, so new height
$= 1.5h$.

New volume
$V' = \pi (0.8r)^2 (1.5h)$

$V' = \pi (0.64r^2)(1.5h)$

$V' = 0.96 \pi r^2 h$

$V' = 0.96V$

Change in volume
$= 0.96V - V = -0.04V$

Percentage change
= -4%

Answer: The volume decreases by 4%.