A cubical box is to be built from iron sheets 1 mm thick. Determine the minimum value of the external edge so that the cube does not sink in water. The density of iron is 8000 kg m ⁻³ and the density of water is 1000 kg m ⁻³ .

Step-by-step solution

Let the external edge of the cubical box be L and the thickness of the iron sheet be t = 1 mm = 0.1 cm . Since the thickness t is very small compared to the edge length L , the volume of the iron used to build the closed cubical box (which has 6 faces) can be approximated as the total surface area multiplied by the thickness: V_ iron 6 L^2 t The mass of the iron box is: m = _ iron V_ iron = _ iron (6 L^2 t) For the cube to just float (not sink), the maximum buoyant force must be equal to the weight of the box. The