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.