Question

A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? Density of iron = 8000 kg/m³ and density of water = 1000 kg/m³.

Answer 1

Let the external Edge of the cubical box  be a m.

Total surface area of the cube = 6a²

The volume of the iron in the box = 6a² ×  1 × 10⁻³

 = 6 × 10⁻³ a² m³

Now, The mass of iron in the box = Volume × density

=  6 × 10⁻³ a² × 8000

=48a² kg

Weight = 48 × 10 = 480 N.

The volume of the water displaced = a³ cm³  [It will be equal to volume of cube displaced].

∴ Upthrust = a³ × 1000 × 10

= 10⁴a³

Now, 10⁴a³ = 480

a = 48 × 10⁻³ m.

Therefore, a = 4.8 cm.

Hope it helps.