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Question

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



A

25%

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B

50%

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C

75%

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D

40%

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Solution

The correct option is C

75%


Let the radius of the old cylinder be R and that of the new cylinder be r.
Then, r=R2

Volume of old cylinder=πR2h

Volume of new cylinder=πr2h
=π×(R2)2×h
=π×R2×h4

Hence, reduction in volume
=Volume of old cylinder - volume of new cylinder
=πR2hπ×R2×h4=34πR2h

Percentage reduction

=Reduction in volumeVolume of old cylinder×100

=34πR2hπR2h×100

=75%


Mathematics

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