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Question

The curved surface area of a cylinder is reduced by ___ percent if the height is half of the original height.

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Solution

The curved surface area of a cylinder with radius r and height h =2πrh
If the height is halved, the new height is h2
Therefore , the new curved surface area of cylinder
=2πr(h2)=πrh

Percentage reduction in curved surface area

=DecreaseOriginal×100%

=2πrhπrh2πrh×100%

=πrh2πrh×100%

=12×100%

=50%

Hence, the curved surface area will reduce by 50% when height will become half.


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