If the heights of two cones are in the ratio | vedclass

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(D) The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Let the heights of the two cones be $h_1$ and $h_2$,and their radii be $r

Vedclass · Accepted Answer

$5:36$

Vedclass · Answer

(D) The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Let the heights of the two cones be $h_1$ and $h_2$,and their radii be $r_1$ and $r_2$.The ratio of their heights is $\frac{h_1}{h_2} = \frac{1}{5}$.Since the ratio of diameters is $5:6$,the ratio of their radii is also $\frac{r_1}{r_2} = \frac{5}{6}$.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 values: $\left(\frac{5}{6}ight)^2 	imes \left(\frac{1}{5}ight) = \frac{25}{36} 	imes \frac{1}{5} = \frac{5}{36}$.Thus,the ratio of their volumes is $5:36$.

If the heights of two cones are in the ratio $1:5$ and their diameters are in the ratio $5:6$,what is the ratio of their volumes?

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