A cubical box is to be constructed with iron sheets 1 mm in thickness

CBSE Class 9
1

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 m-3 and density of water = 1000 kg m-3

2

Let the length of the side of the cube be ‘l’ meters
Volume of the cube = L³
The area of each face of the cube is L²
Considering all the 6 faces of the cube, the weight of the cube is

= 6 × L² × 8000 kg/m³ × 0.001 m
= L² × 48 kg/m²

Weight of the water displaced by the volume of the cube
= L³ × 1000 kg/m³

Condtion for the block not to sink in water is

Weight of the cube = Weight of the water displaced by the volume of the cube
L² × 48 kg/m² = L³ × 1000 kg/m³
On solving we get
L = 48 kg/m² / 1000 kg/m³
L = 0.048 m
L = 48 mm