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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. The number of lead shots dropped in the vessel is :

A
50
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B
25
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C
100
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D
150
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Solution

The correct option is C 100

Let number of lead shots = n


Height of cone =h=8 cm

Radius of cone =r1=5 cm


Volume of water present in the cone = Volume of cone =13.π.(r1)2.h

=(13×227×52×8 cm2)
Volume of water flown out =(14×13×227×52×8) cm3

Radius of lead shot =r=0.5 cm

Volume of each lead shot ... =43.π.r3=(43×227×(0.5)3) cm3

According to question, n lead shots are dropped into the cone such that a quarter of the water present in the cone flows out.
volume of n lead shots = volume of water that flows out

(n×43×227×(0.5)3)=(14×13×227×52×8)

n=14×13×52×8×1(0.53)×34

n=100 .


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