The radius and slant height of a cone are in | vedclass

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(D) Let the radius $r = 5x$ and slant height $l = 13x$.The curved surface area $(CSA)$ of a cone is given by $\pi rl = 1836.9 \, cm^2$.Substituting th

Vedclass · Accepted Answer

$8478$

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(D) Let the radius $r = 5x$ and slant height $l = 13x$.The curved surface area $(CSA)$ of a cone is given by $\pi rl = 1836.9 \, cm^2$.Substituting the values: $3.14 	imes 5x 	imes 13x = 1836.9$.$3.14 	imes 65x^2 = 1836.9$.$204.1x^2 = 1836.9$.$x^2 = \frac{1836.9}{204.1} = 9$.$x = 3$.So,$r = 5 	imes 3 = 15 \, cm$ and $l = 13 	imes 3 = 39 \, cm$.The height $h$ of the cone is $\sqrt{l^2 - r^2} = \sqrt{39^2 - 15^2} = \sqrt{1521 - 225} = \sqrt{1296} = 36 \, cm$.The volume $V$ of the cone is $\frac{1}{3} \pi r^2 h = \frac{1}{3} 	imes 3.14 	imes 15^2 	imes 36$.$V = 3.14 	imes 225 	imes 12 = 3.14 	imes 2700 = 8478 \, cm^3$.

The radius and slant height of a cone are in the ratio of $5:13$. If its curved surface area is $1836.9 \, cm^2$,find its volume. (Use $\pi = 3.14$) (in $cm^3$)

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