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

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(B) Radius of the cone $=$ radius of the hemisphere $= r = 15\, cm$ and slant height of the cone $l = 25\, cm$.For a cone,$l^{2} = r^{2} + h^{2}$.$	h

Vedclass · Accepted Answer

$11775$

Vedclass · Answer

(B) Radius of the cone $=$ radius of the hemisphere $= r = 15\, cm$ and slant height of the cone $l = 25\, cm$.For a cone,$l^{2} = r^{2} + h^{2}$.$	herefore h^{2} = l^{2} - r^{2} = 25^{2} - 15^{2} = 625 - 225 = 400 = (20)^{2}$.So,$h = 20\, cm$.Volume of the combined solid $=$ Volume of the cone $+$ Volume of the hemisphere.Volume $= \frac{1}{3} \pi r^{2} h + \frac{2}{3} \pi r^{3} = \frac{1}{3} \pi r^{2} (h + 2r)$.Substituting the values: Volume $= \frac{1}{3} 	imes 3.14 	imes 15 	imes 15 	imes (20 + 2 	imes 15)$.Volume $= 3.14 	imes 5 	imes 15 	imes (20 + 30) = 3.14 	imes 75 	imes 50 = 3.14 	imes 3750 = 11775\, cm^{3}$.Thus,the volume of the given solid is $11775\, cm^{3}$.

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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