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Surface Areas and Volumes
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30/06/2021 12:36 pm
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A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
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30/06/2021 12:38 pm
For the cone,
Radius = 5 cm,
Height = 8 cm
Radius of sphere = 0.5 cm
Volume of cone = volume of water in the cone
= 1/3πr2h
= (200/3)π cm3
Total volume of water overflown= (1/4) × (200/3) π
=(50/3)π
Volume of lead shot
= (4/3)πr3
= (1/6) π
The number of lead shots = Total Volume of Water over flown/ Volume of Lead shot
= (50/3)π/(1/6)π
= (50/3) × 6 = 100