A hollow cube is to be made from iron sheet of thickness 1 mm. Find the minimum external edge length for which the cube will just float (not sink) in water. (Density of iron = 8000 kg/m³, density of water = 1000 kg/m³.)

32 mm
40 mm
48 mm
52 mm

Correct answer: 48 mm

Solution

The cube just floats when its total weight equals the buoyant force at full submersion: ρ_iron*(iron volume) = ρ_water*a³. For thin walls the iron volume ≈ 6*a²*t. Solving gives a = 6*t*(ρ_iron/ρ_water) = 6*0.001*8 = 0.048 m = 48 mm.

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