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 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.

Answer 1

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
Total volume of water overflown= $(\frac{1}{4})×(\frac{200}{3}) \pi =(\frac{50}{3})\pi$

The volume of lead shot
$= (\frac{4}{3})\pi r^3$
$= (\frac{1}{6}) \pi$

$\text{The number of lead shots}=\frac{\text{Total volume of water overflown}}{\text{Volume of lead shot}}$

$=\frac{ (\frac{50}{3})\pi }{(\frac{1}{6})\pi}$

$= (\frac{50}{3})\times6$
$=100$