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Question

Pavan filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. By how much should the height be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometers and correct up to two decimal places.

___ μm


Solution

Water that will fall out will be equal to the volume of spherical ball dropped into the vessel.

So,

43πr3=πR2H

43×227×0.73=227×72×H

H=0.933333 cm
1 m=106 μm

H=9333.33 μm


Mathematics

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