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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.

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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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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

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