Question

A vessel is in the from of an inverted cone. Its height is $8cm$ and radius of its top which is open is $3cm$. If it is filled with water upto brim. When Lead shots, each of which is sphere of radius $0.5cm$ are dropped into vessel, one fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Answer 1

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

r= 5 cm, h= 8 cm

$u=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 8=\frac{4400}{21}c{m}^2$

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

$=\frac{1}{4}\times \frac{21400}{21}=\frac{1100}{21}c{m}^3$

r= 0.5 cm, volume of 1 lead shot = $\frac{4}{3}\pi r^3=\frac{11}{21}c{m}^3$

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

$=\frac{\frac{1100}{21}}{\frac{11}{21}}=100$