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 of vessel (h) = 8 cm
Radius of vessel (r₁) 5 cm
Radium of lead shots (r₂) = 0.5 cm
Let the number of lead short dropped = n
Therefore, volume of water flows out = n × Volume of 1 lead shot
⇒ 1/4 × Volume of water flow out = n × Volume of 1 lead shot
⇒ 1/4 × 1/3πr₁²h = n × 4/3π³₂
⇒ r²₁h = n × 16 ×r³₂
⇒ 5² × 8 = n × 16 × (0.5)³
⇒ n = (25×8)/(16× (0.5)³ = 100
Hence, the number of lead shots dropped in vessel is 100.