Question

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 rim. 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.

Answer 1

Let no. of lead shots be x

According to the problem,
Volume of lead shots =$\frac{1}{4}\times Volumeofcone$
or, $x\times \frac{4}{3}\times \frac{22}{7}\times 0.5\times 0.5\times 0.5=\frac{1}{4}\times \frac{1}{3}\times \frac{22}{7}\times 8\times 5\times 5x=100$