How many spherical marbles of diameter 2.8 cm should be completely immersed into a cylindrical tank of diameter 14 cm containing some water so that the water level rises by 5.6 cm?

Given: Diameter of the spherical marble = 2.8 cm

Therefore, the radius of the spherical marble (R) = 2.8/2 = 1.4 cm

Diameter of the cylindrical tank = 14 cm

Therefore, the radius of the cylindrical tank (r) = 14/2 = 7 cm

Let n number of spherical marbles be completely immersed into the tank so that the water level rises by 5.6 cm.

Therefore, the volume of n marbles is the same as the volume of the water that rises.

It is known that the volume of the sphere $=\frac{4}{3}{\mathrm{\pi R}}^3$

∴ Volume of n marbles  = $n\times \frac{4}{3}\mathrm{\pi }\times {\left(1.4\right)}^3$

Volume of cylinder $={\mathrm{\pi r}}^2\mathrm{h}$ 

∴ Volume of the water rise = $\mathrm{\pi }{\left(7\right)}^2\times 5.6$ 

The volume of n marbles = Volume of the water rise

$\Rightarrow n\times \frac{4}{3}\mathrm{\pi }\times {\left(1.4\right)}^3=\mathrm{\pi }{\left(7\right)}^2\times 5.6$

$\Rightarrow n=\frac{49\times 5.6\times 3}{4\times 1.4^3}=75$

Thus, 75 marbles should be completely immersed into the tank.