Question

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

Answer 1

Let 'R' and 'h' be the radius and height of the cylinder and 'r' be the radius of sphere.

From the given we can find $R=3.5cm,r=0.7cm$

Let 'n' be the number of spherical marbles that are dropped in a cylindrical vessel.

We need to find level of rise of water level in the vessel that means the volume of water is increasing in cylinder.

Therefore n=$\frac{volumeofwaterdisplaced}{volumeofonesphericalmarble}$

$\therefore n=\frac{\pi R^{2}h}{\frac{4}{3}\pi r^3}=\frac{3R^{2}h}{4r^3}$

$\therefore h=\frac{4\times 150\times {\left(0.7\right)}^3}{{3\times \left(3.5\right)}^2}$

$\therefore h=5.6cm$

Therefore rise in the level of water in the vessel in 5.6 cm