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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.

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Solution

REF.Image
Volume of water flown out = 14 of volume of cone
r= 5 cm, h= 8 cm
u=13πr2h=13×227×5×5×8=440021cm2
Volume of water flown out = 14× volume of cone
=14×2140021=110021cm3
r= 0.5 cm, volume of 1 lead shot = 43πr3=1121cm3
Number of lead shots = volumeofwaterflownoutvolumeof1leadshot
=1100211121=100

1212972_1405903_ans_ddfeea7c5ef64478be3e06831087d999.jpg

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