The ratio of diameters of two cones is 2:3 an | vedclass

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(C) Let the diameters of the two cones be $d_1$ and $d_2$,and their heights be $h_1$ and $h_2$.The ratio of diameters is $d_1:d_2 = 2:3$,so the ratio

Vedclass · Accepted Answer

$1:1$

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(C) Let the diameters of the two cones be $d_1$ and $d_2$,and their heights be $h_1$ and $h_2$.The ratio of diameters is $d_1:d_2 = 2:3$,so the ratio of their radii is $r_1:r_2 = 2:3$.The ratio of their heights is $h_1:h_2 = 9:4$.The volume of a cone is given by $V = \frac{1}{3}\pi r^2 h$.The ratio of their volumes is $\frac{V_1}{V_2} = \frac{\frac{1}{3}\pi r_1^2 h_1}{\frac{1}{3}\pi r_2^2 h_2} = \left(\frac{r_1}{r_2}ight)^2 	imes \left(\frac{h_1}{h_2}ight)$.Substituting the given ratios: $\frac{V_1}{V_2} = \left(\frac{2}{3}ight)^2 	imes \left(\frac{9}{4}ight) = \frac{4}{9} 	imes \frac{9}{4} = 1$.Thus,the ratio of their volumes is $1:1$.

The ratio of diameters of two cones is $2:3$ and the ratio of their heights is $9:4$. Then,the ratio of their volumes is:

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