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Mathematics

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

  1. 2 : 5

  2. 8 : 7

  3. 10 : 9

  4. 16 : 9

Mensuration

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Answer

Given,

r : R = 2 : 3

Let r = 2x and R = 3x

h : H = 5 : 3

Let h = 5y and H = 3y

CSA of 1st cylinderCSA of 2nd cylinder=2πrh2πRH=rhRH=2x×5y3x×3y=10xy9xy=109=10:9\dfrac{\text{CSA of 1st cylinder}}{\text{CSA of 2nd cylinder}} = \dfrac{2π\text{rh}}{2π\text{RH}} \\[1em] = \dfrac{\text{rh}}{\text{RH}} \\[1em] = \dfrac{\text{2x} \times \text{5y}}{\text{3x} \times {\text{3y}}} \\[1em] = \dfrac{10\text{xy}}{9\text{xy}} \\[1em] = \dfrac{10}{9} \\[1em] = 10 : 9

Hence, option 3 is the correct option.

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