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Question
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5: 6, find the ratio of their curved surfaces.
Solution
The ratio in radii of two cylinders = 4 : 3
and ratio in their heights = 5: 6
Let r1 and r2 be the radii and h1,h2 be their heights respectively.
∴ r1 : r2 = 4:3 and h1 : h2 = 5:6
∴ `r_1 = 4/3 "and" (h_1)/(h_2) = 5/6`
∴ Surface area of the first cylinder = `2pir_1h_1`
and area of second cylinder = `2pir_2h_2`
`(2pir_1h_1)/(2pir_2h_2) = r_1/r_2 xx h_1/h_2 = 4/3 xx 5/6 = 20/18`
= `10/9 = 10 : 9`
∴ Ratio in their surface areas = 10 : 9
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