Ice floating in water: submerged fraction

A piece of ice of density 0.9 g/cm³ floats in water of density 1.0 g/cm³. What fraction of its volume is submerged?

Step-by-step

1. V_sub/V = ρ_object/ρ_fluid = 0.9/1 = 90%
   When floating, buoyancy equals weight: ρ_fluid·g·V_sub = ρ_object·g·V
2. ρ_object = 0.9 , ρ_fluid = 1
   Comparing the object's density with the liquid's tells you whether it floats

Why it works

A floating object displaces its own weight, so ρ_water × V_submerged = ρ_ice × V_total. The submerged fraction is therefore the ratio of the two densities.

Common mistakes

• Inverting the ratio and answering 1.0 ÷ 0.9.
• Assuming the ice is fully submerged because its density is close to that of water.

Related

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