A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic sphere of radius 12 cm is dropped into it. What will be the increase in the level of water in the vessel (in cm) ?

9

We know that,

The volume of a cylinder = π × (Radius)² × (Height)

The volume of a sphere = \(\frac{4}{3}\)π (Radius)³

We have,

The diameter of the cylindrical vessel = 32 cm

The radius of the solid metallic sphere = 12 cm

The radius of the cylindrical vessel = \(\frac{32}{2}\) = 16 cm

Let, the height of water increase = a cm

So, π × (16)² × a = \(\frac{4}{3}\) × π × (12)³

= 256a = 2304

= a = 9