Question

A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.

Answer 1

Volume of n lead shots = volume of water displaced.

`n xx 4/3 πr^3 = 2/5 xx 1/3 π R^2 H`

∴ `n = ( 2/5 xx 1/3 π R^2 H)/(4/3πr^3)`

∴ `n = (2R^2H)/(5 xx 4r^3)`

∴ `n = (2 xx 2.5^2 xx 11)/(5 xx 4xx (0.25)^3)`

∴ n = 440 shots.