Question

$150$ spherical marbles, each of diameter $1.4cm$, are dropped in a cylindrical vessel of diameter $7cm$ containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

Answer 1

Diameter of the spherical marble $=1.4$ cm

Radius of the marble $=0.7$ cm

Volume of each marble = $\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (0.7{)}^3=1.44$

Volume of $150$ marbles $=1.44x150=216$ $c{m}^3$

Let the rise in level of water in the cylindrical vessel $=h$ cm

Diameter of the vessel $=7$ cm

Radius of the vessel $=3.5$ cm

Volume of increased level of the water = $\pi r^{2}h=\frac{22}{7}\times {3.5}^2\times h$

Volume of increased level of the water = Volume of $150$ marbles

$\frac{22}{7}\times {3.5}^2\times h=216$

$h=5.6$ cm

Therefore, the rise in the level of water in the vessel $=5.6$ cm.