Answer:
9/10
Step-by-step explanation:
From Archimedes' principle, the buoyant force on the ice equals the weight of water displaced. Since the buoyant force equals the weight of the ice. then
ρ₁V₁g = ρ₂V₂g where ρ₁ = density of ice = 0.9 g/cm³ and V₁ = volume of ice and ρ₂ = density of water = 1 g/cm³ and V₂ = volume of water.
So. ρ₁V₁ = ρ₂V₂
V₁ = ρ₂V₂/ρ₁
= 1 g/cm³V₂/0.9 g/cm³ = 10V₂/9
Now, let x be the fraction of volume of ice submerged. So V = xV₁ = volume submerged. This volume also equals the volume of water since the submerged ice displaces its own volume of water.
So V = V₂
xV₁ = V₂
x(10V₂/9) = V₂
10x/9 = 1
x = 9/10