Question

A vessel in the form of an inverted cone. Its height is $8cm$ and the radius of its top, which is open is $5cm$. It is filled with water upto the brim. When lead shots, each of which is a sphere of radius $0.5cm$ are dropped in the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Answer 1

Number of lead shots = volume of water flown out / volume of 1 lead shot

volume of water flown out $=\frac{1}{4}\times$ volume of cone

Volume of cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{4}\times \frac{4400}{21}=\frac{1100}{21}$

the volume of 1 lead shot = volume of a sphere

Volume of sphere is $\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi (0.5{)}^3=\frac{11}{21}$

Number of lead shots $=\frac{\frac{1100}{21}}{\frac{11}{21}}=100$