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(C) Let the heights of the cylinder and cone be $h_1 = 2x$ and $h_2 = 3x$ respectively.Let the radii of the cylinder and cone be $r_1 = 3y$ and $r_2 =

Vedclass · Accepted Answer

$9:8$

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(C) Let the heights of the cylinder and cone be $h_1 = 2x$ and $h_2 = 3x$ respectively.Let the radii of the cylinder and cone be $r_1 = 3y$ and $r_2 = 4y$ respectively.The volume of a cylinder is given by $V_1 = \pi r_1^2 h_1$.The volume of a cone is given by $V_2 = \frac{1}{3} \pi r_2^2 h_2$.The ratio of their volumes is $\frac{V_1}{V_2} = \frac{\pi r_1^2 h_1}{\frac{1}{3} \pi r_2^2 h_2} = \frac{3 r_1^2 h_1}{r_2^2 h_2}$.Substituting the given ratios: $\frac{V_1}{V_2} = \frac{3 	imes (3y)^2 	imes (2x)}{(4y)^2 	imes (3x)} = \frac{3 	imes 9y^2 	imes 2x}{16y^2 	imes 3x} = \frac{54}{48} = \frac{9}{8}$.Thus,the ratio of their volumes is $9:8$.

$A$ cylinder and a cone have their heights in the ratio $2:3$ and the radii of their bases in the ratio $3:4$. Find the ratio of their volumes.

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