Question

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

Solution

Ratio in radii of two cylinders = 2 : 3 and ratio in their heights = 5 : 3 and radius of the first cylinder (r1)=2x and radius of second cylinder (r2)=3x and height of first cylinder (h1)=5y and height of second of the second cylinder (h2)=3y (i) Now volume of the first cylinder = πr2h =π(2x)2×5y=20πx2y  and volume of the second cylinder  =π(3x)2×3y=π×9x2×3y =27 πx2y Now ratio in their volume = 20πx2y:27πx2y = 20 :  27 (ii) Curved surface area of first cylinder  = 2πrh=2π×2x× 5y = 20 π xy and curved surface  area of second cylinder = 2π×3x×3y=18π xy ∴ Ratio in their curved surface area =20 π xy : 18 π xy = 10 : 9

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