Question : If the radius of a cylinder is decreased by 20% and the height is increased by 20% to form a new cylinder, then the volume will be decreased by:
Option 1: 23.2%
Option 2: 22.3%
Option 3: 32.2%
Option 4: 20.5%
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Correct Answer: 23.2%
Solution :
The volume of a cylinder, $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
If the radius is decreased by 20%, the new radius $r'$ is $0.8r$.
If the height is increased by 20%, the new height $h'$ is $1.2h$.
The volume $V'$ of the new cylinder is $V' = \pi (r')^2 h' = \pi (0.8r)^2 (1.2h) = 0.768 \pi r^2 h$
Percentage change in volume
$=(1-\frac{V'}{V})\times100$
$=(1-0.768)\times100$
$= 23.2\%$
Hence, the correct answer is 23.2%.
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