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Question 10
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.


Solution

Given, diameter of a marble = 1.4 cm
Radius of marble=1.42=0.7 cm
So, volume of one marble  =43π(0.7)343π×0.343=1.3723π cm3
Also given diameter of beaker = 7 cm
Radius of beaker =72=3.5 cm
Height of water level raised = 5.6 cm
Volume of the raised water in breaker
=π(3.5)2×5.6=68.6 π cm3
Now, required number of marbles  =Volume of raised water in beakerVolume of one spherical marble
=68.6π1.372π×3=150

Mathematics

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