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

Question:

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is
(a) 27 : 20
(b) 20 : 27
(c) 4 : 9
(d) 9 : 4

Solution:

(b)  20 : 27

Suppose that the radii of the cylinders are 2r and 3r and their respective heights are 5h and 3h..

$\therefore$ Ratio of their volumes $=\frac{\pi(2 r)^{2} \times 5 h}{\pi(3 r)^{2} \times 3 h}$

$=\frac{4 \times 5}{9 \times 3}=\frac{20}{27}$

 

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