The radius of a cone is 15 , cm and its base | vedclass

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(D) Radius of the cone $=$ radius of the hemisphere $= r = 15 \, cm$.Height of the cone $h = 	ext{Total height} - 	ext{Radius of the hemisphere} = 5

Vedclass · Accepted Answer

$16500$

Vedclass · Answer

(D) Radius of the cone $=$ radius of the hemisphere $= r = 15 \, cm$.Height of the cone $h = 	ext{Total height} - 	ext{Radius of the hemisphere} = 55 - 15 = 40 \, cm$.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 $= \frac{1}{3} 	imes \frac{22}{7} 	imes 15 	imes 15 	imes (40 + 2 	imes 15)$.Volume $= \frac{1}{3} 	imes \frac{22}{7} 	imes 225 	imes (40 + 30) = \frac{1}{3} 	imes \frac{22}{7} 	imes 225 	imes 70$.Volume $= 22 	imes 75 	imes 10 = 16500 \, cm^3$.

The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.

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