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(B) Given:Diameter of the hemisphere $= 14 \, cm$,so radius $r = 14/2 = 7 \, cm$.Total height of the vessel $= 13 \, cm$.Height of the cylindrical par

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$1642.67$

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(B) Given:Diameter of the hemisphere $= 14 \, cm$,so radius $r = 14/2 = 7 \, cm$.Total height of the vessel $= 13 \, cm$.Height of the cylindrical part $h = 	ext{Total height} - 	ext{Radius of hemisphere} = 13 - 7 = 6 \, cm$.Capacity of the vessel $=$ Volume of cylinder $+$ Volume of hemisphere$= \pi r^2 h + \frac{2}{3} \pi r^3$$= \pi r^2 (h + \frac{2}{3} r)$$= \frac{22}{7} 	imes 7 	imes 7 	imes (6 + \frac{2}{3} 	imes 7)$$= 22 	imes 7 	imes (6 + \frac{14}{3})$$= 154 	imes (\frac{18 + 14}{3})$$= 154 	imes \frac{32}{3}$$= \frac{4928}{3} \approx 1642.67 \, cm^3$.

$A$ vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the capacity of the vessel in $cm^3$. (Take $\pi = 22/7$)

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