Question : If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then the volume change is:
Option 1: 52.5%
Option 2: 67.5%
Option 3: 57.5%
Option 4: 62.5%
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Correct Answer: 62.5%
Solution :
The volume of a cylinder
$V = \pi r^2 h$ where $r$ is the radius and $h$ is the height.
The radius of the cylinder is decreased by 50%, the new radius is,
$r' = r - 0.50r = 0.50r$
The height of the cylinder is increased by 50%, the new height is,
$h' = h + 0.50h = 1.50h$
The volume of the new cylinder,
$V' = \pi (r')^2 h' = \pi (0.50r)^2 (1.50h) = 0.375 \pi r^2 h$.
The volume change $=\frac{V - V'}{V} ×100= \frac{\pi r^2 h - 0.375 \pi r^2 h}{\pi r^2 h}×100 = 62.5$%
Hence, the correct answer is 62.5%.
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