A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $7$ cm and the height of the cone is equal to its diameter. Find the volume of the solid.

$Cone surmounted on hemisphere$

Question

A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $7$ cm and the height of the cone is equal to its diameter. Find the volume of the solid.

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Accepted Answer

Step 1: Radius of cone $=$ radius of hemisphere $= 7$ cm. Height of cone $=$ diameter $= 14$ cm.
Step 2: Volume of solid $=$ Volume of hemisphere $+$ Volume of cone $= \frac{2}{3}\pi r^3 + \frac{1}{3}\pi r^2 h$.
Step 3: $= \frac{2}{3} 	imes \frac{22}{7} 	imes (7)^3 + \frac{1}{3} 	imes \frac{22}{7} 	imes (7)^2 	imes 14$.
Step 4: $= \frac{1}{3} 	imes \frac{22}{7} 	imes 7 	imes 7 	imes (14 + 14) = \frac{154}{3} 	imes 28 = \frac{4312}{3}$ cm$^3$ or $1437.33$ cm$^3$.

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