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?

Answer: Option B

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 $$=n\times \frac{4}{3}\pi \times {\left(0.7\right)}^3$$
$$\begin{array}{rl}& \Rightarrow n\times \frac{4}{3}\pi \times {\left(0.7\right)}^3=n\times {\left(\frac{7}{2}\right)}^2\times 5.6\\ & \Rightarrow n\times \frac{4}{3}\times \frac{7}{10}\times \frac{7}{10}\times \frac{7}{10}=\frac{7}{2}\times \frac{7}{2}\times \frac{56}{10}\\ & \Rightarrow n=150\end{array}$$