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A vessel is in the form of an inverted cone. Its height is 8cm and the radius of its top, which is open, is5cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius0.5cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.


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Solution

Step1:Given data

Height of cone (h)=8cm

Radius of cone (r)=5cm

Radius of sphere (R)=0.5cm

Step 2: Find the volume of a cone.

The volume of water = Volume of a cone

=13πr2h=13×π×5×5×8=2003πcm3

The volume of water that flows out=14(total volume of water)

=14×2003π=503πcm3

Step 3: Find the volume of the sphere.

The volume of each sphere =43πr3

=43×π×0.5×0.5×0.5=π6cm3

Step 4: Find the number of lead shots.

Let the number of lead shots be n

Then n=VolumeofWateroverflownVolumeofLeadshot

=503ππ6=50×2=100

n=100spheres

Hence, the number of lead shots are 100.


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