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.

Answer 1

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