The ratio of the diameters of two cylinders i | vedclass

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(D) Let the diameters of the two cylinders be $d_1$ and $d_2$,and their heights be $h_1$ and $h_2$.Given,$d_1:d_2 = 3:4$,so the radii $r_1:r_2 = 3:4$.

Vedclass · Accepted Answer

$9:20$

Vedclass · Answer

(D) Let the diameters of the two cylinders be $d_1$ and $d_2$,and their heights be $h_1$ and $h_2$.Given,$d_1:d_2 = 3:4$,so the radii $r_1:r_2 = 3:4$.Given,$h_1:h_2 = 4:5$.The volume of a cylinder is given by $V = \pi r^2 h$.The ratio of the volumes is $\frac{V_1}{V_2} = \frac{\pi r_1^2 h_1}{\pi r_2^2 h_2} = \left(\frac{r_1}{r_2}ight)^2 	imes \left(\frac{h_1}{h_2}ight)$.Substituting the given ratios: $\frac{V_1}{V_2} = \left(\frac{3}{4}ight)^2 	imes \left(\frac{4}{5}ight) = \frac{9}{16} 	imes \frac{4}{5} = \frac{9 	imes 1}{4 	imes 5} = \frac{9}{20}$.Thus,the ratio of their volumes is $9:20$.

The ratio of the diameters of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..... .

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