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Answer :
Height of the conical vessel, h = 8 cm.
Its radius r = 5 cm
Volume of cone = Volume of water in cone \(= \ \frac{1}{3} \pi r^2 h \)
\(= \ \frac{1}{3} \ × \ \frac{22}{7} \ × \ 5 \ × \ 5 \ × \ 8 \ = \ \frac{4400}{21} \) cm3
Volume of water flows out = Volume of lead shots
\( = \ \frac{1}{4} \) of the volume of water in the cone
\( = \ \frac{1}{4} \ × \ \frac{4400}{21} \ = \ \frac{1100}{21} \) cm3
Radius of the lead shot = 0.5 cm
Volume of one spherical lead shot \(= \ \frac{4}{3} \pi r^3 \ = \ \frac{4}{3} \ × \ \frac{22}{7} \ × \ ( \frac{5}{10})^3 \)
\(= \ \frac{11}{21} \) cm3
\(\therefore \) Number of lead shots dropped into the vessel
\( = \frac{ \ Volume \ of \ water \ flows \ out}{Volume \ of \ one \ lead \ shot} \ = \frac{ \frac{1100}{21}}{ \frac{11}{21}} \)
\( = \ \frac{1100}{21} \ × \ \frac{21}{11} \ = \ 100 \)