The curved surface area of a cone is 550 , cm | vedclass

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(B) Given for a cone: radius $(r) = 7 \, cm$ and curved surface area $= 550 \, cm^2$.The formula for the curved surface area of a cone is $\pi r l$.Th

Vedclass · Accepted Answer

$1232$

Vedclass · Answer

(B) Given for a cone: radius $(r) = 7 \, cm$ and curved surface area $= 550 \, cm^2$.The formula for the curved surface area of a cone is $\pi r l$.Therefore,$550 = \frac{22}{7} 	imes 7 	imes l$.$550 = 22 	imes l \implies l = \frac{550}{22} = 25 \, cm$.Using the relation $l^2 = r^2 + h^2$,we find the height $(h)$:$h^2 = l^2 - r^2 = (25)^2 - (7)^2 = 625 - 49 = 576$.$h = \sqrt{576} = 24 \, cm$.The volume of a cone is given by $V = \frac{1}{3} \pi r^2 h$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes 7 	imes 7 	imes 24$.$V = 22 	imes 7 	imes 8 = 1232 \, cm^3$.

The curved surface area of a cone is $550 \, cm^2$. If the radius of the cone is $7 \, cm$,find its volume in $cm^3$.

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