A vessel is in the form of an inverted cone. Its height is $$8$$ cm and radius of its top is $$5$$ cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius $$0.5$$ cm are dropped into the vessel, $$14$$ of the water flows out. Then the number of lead shots dropped into the water is

Question

A vessel is in the form of an inverted cone. Its height is $$8$$ cm and radius of its top is $$5$$ cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius $$0.5$$ cm are dropped into the vessel, $$14$$ of the water flows out. Then the number of lead shots dropped into the water is

Infinity Learn · Accepted Answer

n× volume of sphere  $$=14$$ volume of cone⇒n×$$43$$$$π$$$$r3=14$$.π$$R2H3$$⇒n×$$43.510.510.510=14.5.5.83$$⇒$$n=14.5.5.83.34.105.105.105$$⇒$$n=100$$

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