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, 1/4 of the water flows out. Find the number of lead shots dropped in the vessel.

Given:
Height (h) of conical vessel = 8 cm
Radius (r1) of conical vessel = 5 cm
Radius (r2) of lead shots = 0.5 cm
Let x be the number of lead shots dropped in the vessel.
Volume of the cone = (1/3)π(r1)²h
Volume of water spilled = Volume of dropped lead shots
According to the question
(1/4) × (1/3)πr₁²h = x × (4/3) × πr₂³
=> r₁²h = x × 16r₂³
=> 5² × 8 = x × 16 × (0.5)³
=> 200 = x × 2
=> x = 200/2
=> x = 100.
Therefore, the number of lead shots dropped in the vessel is 100.