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Question

The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their curved surface areas.

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Solution

In two cylinders,

Ratio in radii of two cylinders =2:3
Ratio in their heights =5:3
Let r1 and r2 be the radii and h1,h2 be their heights respectively.
r1:r2=2:3 and h1:h2=5:3
r1r2=23 and h1h2=53

Since, Surface area of the first cylinder =2πrh square units
The ratio of surface area of the two cylinders
=2πr1h12πr2h2

=r1h1r2h2

=r1r2×h1h2

=23×53

=109
Hence, the ratio in their surface areas =10:9


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