Given, diameter of the vessel = 12 cm

So, radius of the vessel = 12/2 = 6 cm

Now, volume of the sphere = (4/3)π r 3

= (4/3)π × 6 3

= (4/3)π × 6 × 6 × 6

= 4 × π × 6 × 6 × 2 = 288π

Now, water displaced is equal to the volume of the sphere

Given, level of the water increased h = 3 (5/9) = 32/9

The shape of the given to be cylindrical.

Let r is the radius of the cylinder.

Now, volume of the water displaced = 288π

⇒ π r 2 h= 288π

⇒ r 2 × 32/9= 288

⇒ r 2 = (288 × 9)/32

⇒ r 2 = 9*9

⇒ r 2 = 81

⇒ r = √81

⇒ r = 9

Hence, diameter of the cylinder = 2r = 2 × 9 = 18 cm

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