A sphere of diameter 5 cm is dropped into a cylindrical

Radius of sphere $r=\frac{5}{2} \mathrm{~cm}$, radius of cylindrical vessel $r_{1}^{2}=\frac{10}{2} \mathrm{~cm}$.

When the sphere is completely submerged into the vessel. The level of water will be raised let x be height of level of raised water.

Therefore,

The volume of raised water in cylindrical vessel = volume of sphere

$25 x=\frac{4 \times 125}{3 \times 8}$

$x=\frac{4 \times 125}{3 \times 8 \times 25}$

$=\frac{5}{6} \mathrm{~cm}$

$x=\frac{5}{6} \mathrm{~cm}$

Hence, the level of water rise $=\frac{5}{6} \mathrm{~cm}$