The radius of the base of a cone is 14 , cm a | vedclass

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(D) Given: Radius of the base $(r)$ = $14 \, cm$,Slant height $(l)$ = $50 \, cm$.First,we find the vertical height $(h)$ of the cone using the relatio

Vedclass · Accepted Answer

$9856$

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(D) Given: Radius of the base $(r)$ = $14 \, cm$,Slant height $(l)$ = $50 \, cm$.First,we find the vertical height $(h)$ of the cone using the relation $r^2 + h^2 = l^2$.$14^2 + h^2 = 50^2$$196 + h^2 = 2500$$h^2 = 2500 - 196 = 2304$$h = \sqrt{2304} = 48 \, cm$.The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes 14 	imes 14 	imes 48$$V = \frac{1}{3} 	imes 22 	imes 2 	imes 14 	imes 48$$V = 22 	imes 2 	imes 14 	imes 16$$V = 9856 \, cm^3$.Therefore,the volume of the cone is $9856 \, cm^3$.

The radius of the base of a cone is $14 \, cm$ and its slant height is $50 \, cm$. Find the volume of the cone (in $cm^3$).

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