Question

Marbles of diameter 1.4 cm are dropped into a
beaker containing some water and are fully
submerged. The diameter of the beaker is 7 cm.
Find how many marbles have been dropped in it
if the water rises by 5.6 cm.
​

Answer 1

Diameter of marble = 1.4 cm

So, radius = 1.4/2 = 0.7 cm

Volume of 1 marble = $\frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (0.7^{3} )$

Let number of marbles required = x

=>Base diameter of beaker = 7cm

Radius of base = 7/2 = 3.5 cm

Rise in level of water = 5.6 cm

Volume change = volume of x marbles

$\pi r^{2} h= x (\frac{4}{3} ) \pi r^{3}$

=> $\pi (3.5^{2}) (5.6) =x (\frac{4}{3} ) \pi (0.7^{3} )$

Solving

x= 150

So 150 marbles should be dropped.