Q. 173.8( 8 Votes )
A vessel is in the form of a hemispherical bowl surmounted by a hallow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.
Answer :
Vessel is in the form of a hemispherical bowl surmounted by a hallow cylinder.
Diameter of hemisphere = 21 cm
Radius of hemisphere = 10.5 cm
Volume of hemisphere = 2/3 πr3 = 2/3 × 22/7 × 10.53 cm3
= 2425.5 cm3
Total height of vessel = 14.5 cm
Height of cylinder = h = Total height of vessel - Radius of hemisphere
= 14.5 – 10.5 cm = 4 cm
Volume of cylinder = πr2h = 22/7 × 10.5 × 10.5 × 4 cm3
= 1386 cm3
Volume of vessel = Volume of hemisphere + Volume of cylinder
= 2425.5 cm3 + 1386 cm3
= 3811.5 cm3
∴ Capacity of vessel = 3811.5 cm3
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