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.
Height (h) of conical vessel = 8 cm
Radius (r1) of conical vessel = 5 cm
Radius (r2) of lead shots = 0.5 cm
Let n number of lead shots were dropped in the vessel.
Volume of water spilled = Volume of dropped lead shots
`1/4 xx "Volume of cone" = n xx 4/3 r_2^3`
`1/4xx1/3pir_1^2h = n xx 4/3pir_2^3`
`r_1^2h = n xx 16r_2^3`
`5^2xx8 = nxx 16xx (0.5)^3`
`n = (25xx8)/(16xx(1/2)^3) = 100`
Hence, the number of lead shots dropped in the vessel is 100.