The base of a cone with radius 15 , cm and sl | vedclass

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(A) Given: Radius of the cone $(r)$ = $15 \, cm$,Slant height $(l)$ = $25 \, cm$.First,find the height $(h)$ of the cone using the relation $l^2 = r^2

Vedclass · Accepted Answer

$11775$

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(A) Given: Radius of the cone $(r)$ = $15 \, cm$,Slant height $(l)$ = $25 \, cm$.First,find the height $(h)$ of the cone using the relation $l^2 = r^2 + h^2$.$h^2 = 25^2 - 15^2 = 625 - 225 = 400$.$h = \sqrt{400} = 20 \, cm$.Volume of the cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} 	imes 3.14 	imes 15^2 	imes 20 = 3.14 	imes 225 	imes \frac{20}{3} = 3.14 	imes 75 	imes 20 = 3.14 	imes 1500 = 4710 \, cm^3$.Volume of the hemisphere = $\frac{2}{3} \pi r^3 = \frac{2}{3} 	imes 3.14 	imes 15^3 = \frac{2}{3} 	imes 3.14 	imes 3375 = 2 	imes 3.14 	imes 1125 = 7065 \, cm^3$.Total volume of the solid = Volume of cone + Volume of hemisphere = $4710 + 7065 = 11775 \, cm^3$.

The base of a cone with radius $15 \, cm$ and slant height $25 \, cm$ is hemispherical. Find the volume of this solid. $(\pi = 3.14)$ (in $cm^3$)

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