Question

A vessel 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 upto the brim. when lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, 1 4 th of the water flows. out. find the number of lead shots

Answer 1

Volume of water in the cone
$\frac{1}{3} \times \pi \times {5}^{2} \times 8 = \frac{200}{3} \times \pi$
1/4th of this water = 50 / 3 × π
If number of lead shots is 'n',
Total volume of lead shots = Water flowed out
$n \times \frac{4}{3} \pi \times {0.5}^{3} = \frac{50}{3} \times \pi$
$n = 100$