The ratio of radii of two cylinders with equa | vedclass

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(D) Let the radii of the two cylinders be $r_1$ and $r_2$,and their heights be $h_1$ and $h_2$. Given that $h_1 = h_2 = h$ and $r_1:r_2 = 4:5$.The vol

Vedclass · Accepted Answer

$16:25$

Vedclass · Answer

(D) Let the radii of the two cylinders be $r_1$ and $r_2$,and their heights be $h_1$ and $h_2$. Given that $h_1 = h_2 = h$ and $r_1:r_2 = 4:5$.The volume of a cylinder is given by the formula $V = \pi r^2 h$.The ratio of their volumes is $\frac{V_1}{V_2} = \frac{\pi r_1^2 h}{\pi r_2^2 h} = \frac{r_1^2}{r_2^2} = \left(\frac{r_1}{r_2}\right)^2$.Substituting the given ratio: $\frac{V_1}{V_2} = \left(\frac{4}{5}\right)^2 = \frac{16}{25}$.Therefore,the ratio of their volumes is $16:25$.

The ratio of radii of two cylinders with equal height is $4:5$. What is the ratio of their volumes?

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