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

Question

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

= Volumeof old cylinder - volume ofnew 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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