Question

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.

Answer 1

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]

Therefore, 150 marbles are required.