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
