The ratio of the radius and slant height of a | vedclass

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(C) For a given cone,the curved surface area $= 423.9 \, cm^2$.Radius : slant height $= 3:5$.Let the radius be $r = 3x \, cm$ and the slant height be

Vedclass · Accepted Answer

$1017.36$

Vedclass · Answer

(C) For a given cone,the curved surface area $= 423.9 \, cm^2$.Radius : slant height $= 3:5$.Let the radius be $r = 3x \, cm$ and the slant height be $l = 5x \, cm$.The curved surface area of a cone is given by $\pi rl$.Therefore,$423.9 = 3.14 	imes 3x 	imes 5x$.$423.9 = 3.14 	imes 15x^2$.$x^2 = \frac{423.9}{47.1} = 9$.So,$x = 3$.Thus,radius $r = 3(3) = 9 \, cm$ and slant height $l = 5(3) = 15 \, cm$.Using the relation $l^2 = h^2 + r^2$,we find the height $h$:$h^2 = l^2 - r^2 = 15^2 - 9^2 = 225 - 81 = 144$.$h = \sqrt{144} = 12 \, cm$.The volume of a cone is $V = \frac{1}{3} \pi r^2 h$.$V = \frac{1}{3} 	imes 3.14 	imes 9^2 	imes 12$.$V = 3.14 	imes 81 	imes 4 = 1017.36 \, cm^3$.

The ratio of the radius and slant height of a cone is $3:5$ and its curved surface area is $423.9 \, cm^2$. Find its volume. $(\pi = 3.14)$ (in $cm^3$)

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