Question

A vessel is in the form of an inverted cone. its height is $8cm$ and the radius of its top, which is open ,$5cm$. it is filled with water up to the brim. when lead shots each of which is a sphere of radius $0.5cm$ are dropped into the vessel,one-fourth of water flows out. find the number of lead shots dropped in the vessel.

Answer 1

Given,

radius of cone$=r=5$cm

Height of cone$=h=8$cm

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

$=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 8$

$=\frac{4400}{21}c{m}^3$

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

$=\frac{1100}{21}c{m}^3$

Volume of $1^{st}$ lead shot$=$volume of sphere read $=0.5$cm

Volume$=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \frac{22}{7}\times (0.5{)}^3$

$=\frac{11}{21}c{m}^3$

Now,

Number of lead shots$=\frac{volumeflownout}{volumeof1leadshot}$

$=\frac{1100/21}{11/21}$

$=100$

Therefore there are $100$ lead shots.