M.L Aggarwal book Important Question of class 10 chapter Based on Mensuration for ICSE BOARD.

A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top, which is open, is 2.5 cm. It is filled with water upto the rim.

Find the number of lead shots dropped into the vessel.

This is the Question Number 25, Exercise 17.5 of M.L Aggarwal.

Deepak BoraNewbie

# A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top, which is open, is 2.5 cm. It is filled with water upto the rim. When some lead shots, each of which is a sphere of radius 0.25 cm, are dropped into the vessel, 2/5 of the water flows out. Find the number of lead shots dropped into the vessel.

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Given height of the cone, h = 11 cmRadius of the cone, r = 2.5 cmVolume of the cone = (1/3)r^{2}h= (1/3)Ã—2.5^{2}Ã—11= (11/3)Ã—6.25 cm^{3}When lead shots are dropped into vessel, (2/5) of water flows out.Volume of water flown out = (2/5)Ã—(11/3)Ã—6.25= (22/15)Ã—6.25= (137.5/15) cm^{3}Radius of sphere, R = 0.25 cm = Â¼ cmVolume of sphere = (4/3)R^{3}= (4/3)Ã—(1/4)^{3}= /48 cm^{3}Number of lead shots dropped = Volume of water flown out/ Volume of sphere= (137.5/15) Ã·/48= (137.5/15) Ã—48/= 137.5Ã—48/15= 440Hence the number of lead shots dropped is 440.