Balls of marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and 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?

Solution (By Examveda Team)

Diameter of beaker = 7 cm
Radius = $$\frac{7}{2}$$ cm
Level of water rises = 5.6 cm
Diameter of a marble = 1.4 cm
∴ Radius = $$\frac{{1.4}}{2}$$ = 0.7 cm
Let n marbles are dropped so,
Volume of n marbles $$ = n \times \frac{4}{3}\pi \times {\left( {0.7} \right)^3}$$
$$\eqalign{ & \Rightarrow n \times \frac{4}{3}\pi \times {\left( {0.7} \right)^3} = n \times {\left( {\frac{7}{2}} \right)^2} \times 5.6 \cr & \Rightarrow n \times \frac{4}{3} \times \frac{7}{{10}} \times \frac{7}{{10}} \times \frac{7}{{10}} = \frac{7}{2} \times \frac{7}{2} \times \frac{{56}}{{10}} \cr & \Rightarrow n = 150 \cr} $$