A vessel is in the form of an inverted cone. | vedclass

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(A) Height $(h)$ of the conical vessel $= 8 \, cm$.Radius $(r_1)$ of the conical vessel $= 5 \, cm$.Radius $(r_2)$ of each lead shot $= 0.5 \, cm$.Let

Vedclass · Accepted Answer

$100$

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(A) Height $(h)$ of the conical vessel $= 8 \, cm$.Radius $(r_1)$ of the conical vessel $= 5 \, cm$.Radius $(r_2)$ of each lead shot $= 0.5 \, cm$.Let $n$ be the number of lead shots dropped into the vessel.According to the problem,the volume of water that flows out is equal to the total volume of the lead shots dropped.Volume of water spilled $= \frac{1}{4} 	imes$ Volume of the cone.$\frac{1}{4} 	imes (\frac{1}{3} \pi r_1^2 h) = n 	imes (\frac{4}{3} \pi r_2^3)$.Canceling $\frac{1}{3} \pi$ from both sides:$\frac{1}{4} r_1^2 h = 4 n r_2^3$.$r_1^2 h = 16 n r_2^3$.Substituting the values:$5^2 	imes 8 = 16 	imes n 	imes (0.5)^3$.$25 	imes 8 = 16 	imes n 	imes (\frac{1}{2})^3$.$200 = 16 	imes n 	imes \frac{1}{8}$.$200 = 2n$.$n = 100$.Thus,the number of lead shots dropped in the vessel is $100$.

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