If the radius of a cylinder is reduced by 50%, then the volume of the cyl

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If the radius of a cylinder is reduced by 50%, then the volume of the cylinder will be reduced by_____.

Options:

A . 25%

B . 50%

C . 75%

D . 40%

Answer: Option C
:
C

Let the radius of the old cylinder be $R$ and that of the new cylinder be $r$ .
$Then, r = \frac{R}{2}$
$Volume of old cylinder = π R^{2} h$
$Volume of new cylinde r = π r^{2} h$
$= π \times (\frac{R}{2})^{2} \times h$
$= \frac{π \times R^{2} \times h}{4}$
Hence, reduction in volume
$= Volume of old cylinder - volume of new cylinder$
$= π R^{2} h - \frac{π \times R^{2} \times h}{4} = \frac{3}{4} π R^{2} h$
$∴$ Percentage reduction
$= \frac{Reduction in volume}{Volume of old cylinder} \times 100$
$= \frac{\frac{3}{4} π R^{2} h}{π R^{2} h} \times 100$
$= 75 %$

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