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.


Let x no of marbles are dropped, so that water level rises by 5.6 cm.


The increase in volume of water in beaker = Volume of x marbles.


Now,


Required raise in height, h = 5.6 cm


Diameter of beaker = 7 cm


Radius of beaker, r = 3.5 cm


[Radius = diameter/2]


Required increase in volume = volume of cylinder of above dimensions = πr2h


[As volume of cylinder = πr2h,


where r = Base radius and h = height]


Required increase in volume = π(3.5)2(5.6) cm3


Now, As diameter of marble is 1.4 cm


Radius of marble, r = 0.7 cm


[As radius = diameter/2]




So, we have,





Therefore, 150 marbles are required.


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