If a right circular cone of height 24, cm has | vedclass

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(A) Let the radius of the cone be $r\, cm$.Given height $h = 24\, cm$ and volume $V = 1232\, cm^{3}$.The formula for the volume of a cone is $V = \fra

Vedclass · Accepted Answer

$550$

Vedclass · Answer

(A) Let the radius of the cone be $r\, cm$.Given height $h = 24\, cm$ and volume $V = 1232\, cm^{3}$.The formula for the volume of a cone is $V = \frac{1}{3} \pi r^{2} h$.Substituting the values: $\frac{1}{3} 	imes \frac{22}{7} 	imes r^{2} 	imes 24 = 1232$.$r^{2} = \frac{1232 	imes 3 	imes 7}{22 	imes 24} = 49$.Therefore,$r = \sqrt{49} = 7\, cm$.The slant height $l$ is given by $l = \sqrt{h^{2} + r^{2}} = \sqrt{24^{2} + 7^{2}} = \sqrt{576 + 49} = \sqrt{625} = 25\, cm$.The curved surface area of the cone is $\pi r l = \frac{22}{7} 	imes 7 	imes 25 = 22 	imes 25 = 550\, cm^{2}$.

If a right circular cone of height $24\, cm$ has a volume of $1232\, cm^{3},$ then the area (in $cm^{2}$) of its curved surface is:

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