Question

A cubical box is to be constructed with iron sheets of 1 mm thickness. What can be the minimum value of the external edge so that the cube does not sink in water ? Density of iron = 8000kgm^3 and Density of water = 1000kgm^3.

Answer 1

Let the minimum value of external edge is x mm. so, internal edge is (x -2) mm

hence, total volume of cubical box = eternal volume - internal volume
=[ x³ - (x - 2)³] mm³

mass of cubical box = V × density × g
= [x³ - (x - 2)³ ] × 8000 × g

volume of water displaced by box = x³ mm³
mass of water displaced by box = V× density' × g
= x³ × 1000 × g

for the cube doesn't sink ,
mass of cubical box = mass of water displaced by box ,
[x³ - (x - 2)³ ] × 8000 × g == x³ × 1000 × g
8[x³ - (x -2)³ ] = x³
=> 8x³ - 8(x -2)³ = x³
=> 7x³ = 8(x -2)³
³√7 x = 2(x -2)
1.91x = 2x - 4
2x - 1.91x = 4 =>, 0.09x = 4
x = 44.4 mm

hence, minimum value of external edge = 44.4mm