The ratio of radii of two cylinders is 3:4 an | vedclass

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Question

(B) The volume of a cylinder is given by the formula $V = \pi r^2 h$.Let the radii of the two cylinders be $r_1$ and $r_2$,and their heights be $h_1$

Vedclass · Accepted Answer

$9:20$

Vedclass · Answer

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

The ratio of radii 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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