As, the sphere fits exactly in the cylinder, the radius of the sphere should be equal to the radius of the cylinder.

Let ‘R’ be the radius of the cylinder and the sphere.

⇒ The height of the cylinder = 2R (? Height of the cylinder will be equal to the diameter of the sphere i.e., 2R)

Volume of the cylinder = π × (radius)² × (height)

⇒ Volume of the cylinder = π × R² × 2R = 2πR³

Volume of the sphere = (4/3) × π × (radius)³

⇒ Volume of the sphere = (4/3) π R³

Volume of water in the gap between cylinder and sphere

 = Volume of cylinder – Volume of sphere

⇒ 2πR³ – (4/3) π R³

⇒ (2/3)π R³

Since, the cross-section of cylindrical can is a circle, the area of cross - section of the cylindrical can must be equal to the area of the circle with radius equal to the radius of the cylindrical can.

⇒ Area of cross - section of the cylindrical can = π R²

Depth of water in the can before the sphere is put

 = (Volume of water)/(Area of cross - section of the cylindrical can)

⇒ 2 π R³/3 π R²

⇒ 2R/3

As, per the question, R = 5.7 cm.