The radii of two cylinders are in the ratio 2 | vedclass

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(A) Let the radii of the two cylinders be $r_1 = 2x$ and $r_2 = 3x$.Let the heights of the two cylinders be $h_1 = 5y$ and $h_2 = 3y$.The volume of a

Vedclass · Accepted Answer

$20:27$

Vedclass · Answer

(A) Let the radii of the two cylinders be $r_1 = 2x$ and $r_2 = 3x$.Let the heights of the two cylinders be $h_1 = 5y$ and $h_2 = 3y$.The volume of a cylinder is given by the formula $V = \pi r^2 h$.The ratio of their volumes is $\frac{V_1}{V_2} = \frac{\pi r_1^2 h_1}{\pi r_2^2 h_2}$.Substituting the values: $\frac{V_1}{V_2} = \frac{\pi (2x)^2 (5y)}{\pi (3x)^2 (3y)}$.$= \frac{\pi (4x^2) (5y)}{\pi (9x^2) (3y)}$.$= \frac{20 \pi x^2 y}{27 \pi x^2 y}$.$= \frac{20}{27}$.Thus,the ratio of their volumes is $20:27$.

The radii of two cylinders are in the ratio $2:3$. The ratio of their heights is $5:3$. The ratio of their volumes is:

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