# A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3 5/9 cm. Find the diameter of the cylindrical vessel.

Given:

Increase in the height of the cylinder due to the sphere, h = 3 5/9 = 32/9 cm

Diameter of the sphere = 12 cm

Radius of the sphere = 6 cm = R

Rise in the water volume in cylinder = volume of sphere

πr<sup>2</sup>h = 4/3πR<sup>3</sup>

$$\begin{array}{l}r=sqrt{frac{4times 6^{3}times 9}{3times 32}}\end{array}$$

r = 9 cm

Therefore, the diameter of the cylindrical vessel = 18 cm