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Question
A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.
Sum
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Solution
Diameter of the hemisphere = 21 cm
Therefore, radius of the hemisphere = 10.5 cm
Volume of the hemisphere `=2/3pir^3= 2/3xx22/7xx 10.5xx 10.5xx10.5 = 2425.5 "cm"^3`
Height of the cylinder
= Total height of the vessel - Radius of the hemisphere = 14.5 - 10.5= 4 cm
Volume of the cylinder = `pir^2h = 22/7xx10.5xx10.5xx4=1386 "cm"^3`
Total Volume= Volume of hemispherical part + Volume of cylinder = 1386 + 2425.5 = 3811.5 cm3
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