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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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