A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?
(Given: density of water = 1000 kg m⁻³)

Solution

Physics sir · 3 steps

A floating cube displaces exactly its own weight of water, so 400 g of cube sinks 400 cm³ of itself.

1. Floating condition. A floating body is in equilibrium, so the buoyant force equals its weight. The weight of water displaced equals the weight of the cube.

   ρ_w Vᵢₙ g = m g ⇒ Vᵢₙ = m/ρ_w = (400 g)/(1 g cm⁻³) = 400 cm³

2. Total volume. The edge is 10 cm, so the cube's volume is 10³ = 1000 cm³. The water density 1000 kg m⁻³ is the same as 1 g cm⁻³.
3. So. Volume outside = 1000 - 400 = 600 cm³, which is option (b).

The idea to keep. For anything floating, the submerged volume is mass divided by liquid density. Subtract it from the total volume to get the part above the surface.

Answer from the NTA final answer key. Solution by PrepWiser.