Question

3. 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

Given,

Radius of cone = r = 5 cm

Height of cone = h = 8 cm

Volume of cone

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

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

$= \frac{4400}{21} {cm}^{3}$

Volume of water flows out

$= \frac{1}{4} \times volume \: of \: cone$

$= \frac{1100}{21} {cm}^{3}$

Volume of 1st lead shot = Volume of sphere read = 0.5cm

Volume

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

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

$= \frac{11}{21} {cm}^{3}$

Now,

Number of lead shots

$= \frac{volume \: flown \: out}{volume \: of \: 1 \: lead \: shot}$

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

$= 100$

Therefore there are 100 lead shots