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Question
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Solution
Height of cone = 8 cm
Radius = 5 cm
Volume = `1/3pir^2h`
= `1/3 xx 22/7 xx 5 xx 5 xx 8 cm^3`
= `4400/21 cm^3`
Therefore, volume of water that flowed out
= `1/4 xx 4400/21 cm^3`
= `1100/21 cm^3`
Radius of each ball = 0.5 cm = `1/2` cm
Volume of a ball = `4/3pir^3`
= `4/3 xx 22/7 xx 1/2 xx 1/2 xx 1/2 cm^3`
= `11/21 cm^3`
Therefore, No. of balls = `1100/21 ÷ 11/21 = 100`
Hence, number of lead balls = 100
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