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Question

If the radius of a cylinder is doubled and height is halved find the change in the volume.

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Solution

Let the radius of the cylinder be r and height be h.

Then, volume of the cylinder,
V1=πr2h


New radius, R=2r

New height of the cylinder, H=h2

Volume of a cylinder,
V2=πR2H=π(2r)2h2

=π×4r2×h2

=2πr2h

=2V1

Hence, if the radius of a cylinder is doubled and height of a cylinder is halved, the volume of the cylinder is doubled.


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