Marbles of diameters 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 beaker so that the water level rises by 5.6 cm.

Given,


Diameter of marble = 1.4 cm


Diameter of cylinder = 7 cm


Radius of cylinder = 3.5 cm


Cylinder height = 5.6 cm


Radius of marble = 0.7 cm


Volume of 1 marble = πr3


= = 1.4373


So,


Let the number of marbles be n,


Increase in the Volume of cylinder due to n marbles = πr2h


= 3.14 × 3.5 × 3.5 × 5.6 = 215.6 cm3


Hence the total numbers of marble required = = 150 marbles


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