If a hemisphere of radius 3 cm is fitted inside a cuboid and then water is filled inside the cuboid, the amount of water (in cm³) present in the cuboid is:
(Take π = 3.14)

Given:

Radius of hemisphere (r) = 3 cm

Volume of water in the cuboid = Volume of cuboid - Volume of hemisphere

Formula used:

Volume of cuboid = Length × Breadth × Height

Volume of hemisphere = (2/3)πr³

Calculation:

Since the hemisphere is fitted inside the cuboid, the diameter of the hemisphere is equal to the smallest dimension of the cuboid. Therefore:

Diameter of hemisphere = 2 × r = 2 × 3 = 6 cm

Minimum possible dimensions of the cuboid: 

Height = Radius of hemisphere = 3 cm

Length = Diameter of cuboid = 6 cm

Breadth = Diameter of cuboid = 6 cm

Volume of cuboid = 6 × 6 × 3 = 108 cm³

Volume of hemisphere = (2/3) × 3.14 × 3³

⇒ Volume of hemisphere = (2/3) × 3.14 × 27

⇒ Volume of hemisphere = 56.52 cm³

Volume of water in the cuboid = Volume of cuboid - Volume of hemisphere

⇒ Volume of water = 108 - 56.52

⇒ Volume of water = 51.48 cm³

∴ The correct answer is option (4).