### Question 9

SSC-CGL 2020 Mar 3 Shift 1

Radii of two cylinders are in the ratio 4 : 5 and their heights are in the ratio 9 : 8. The ratio of their volumes is?

### Solution in Brief

Volume of a cylinder is proportional to $\displaystyle R^2H$, so the ratio of their volumes is (4 x 4 x 9) : (5 x 5 x 8), which simplifies to 18 : 25 answer!

### Solution in Detail

[1] Ratio of radii given $\displaystyle \frac{R_1}{R_2} = \frac{4}{5} $

[2] Ratio of heights given $\displaystyle \frac{H_1}{H_2} = \frac{9}{8} $

$\displaystyle \therefore$ Ratio of volumes is: $\displaystyle \frac{\pi R_1^2 H_1}{\pi R_2^2 H_2}$

$\displaystyle \therefore \:= \bigg(\frac{R_1}{R_2}\bigg)^2 \times \bigg(\frac{H_1}{H_2}\bigg)$

$\displaystyle = \bigg(\frac{4}{5}\bigg)^2 \times \bigg(\frac{9}{8}\bigg) = 18 : 25 \:\underline{Ans}$

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