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 ______.
Answer: Option A
:
A
Let number of lead shots = n
Height of cone =h=8cm
Radius of cone =r1=5cm
Volume of water present in the cone = Volume of cone =13.π.(r1)2.h
=(13×227×52×8cm2)
Volume of water flown out =(14×13×227×52×8)cm3
Radius of lead shot =r=0.5cm
Volume ofeach lead shot ... =43.π.r3=(43×227×(0.5)3)cm3
According to given situation, n lead shots are thrown into cone such that 1/4thof water presentin cone flows out.
It means volume of n lead shots = volume of water flown 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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:
A
Let number of lead shots = n
Height of cone =h=8cm
Radius of cone =r1=5cm
Volume of water present in the cone = Volume of cone =13.π.(r1)2.h
=(13×227×52×8cm2)
Volume of water flown out =(14×13×227×52×8)cm3
Radius of lead shot =r=0.5cm
Volume ofeach lead shot ... =43.π.r3=(43×227×(0.5)3)cm3
According to given situation, n lead shots are thrown into cone such that 1/4thof water presentin cone flows out.
It means volume of n lead shots = volume of water flown 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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