Hey!

Let the edge length of the cube  = a

Radius of atom = r

In a simple cube  numbers of atoms present = (1/8)*8=1

Then volume occupied = 1*(4/3) π r 3

Atoms are at corner in a simple cube and are touching each other. Which means a=2r

That is r=a/2

Volume of cube = a^3

Fraction of total volume =[( 4/3) π r^3. ] / a^3

By putting r=a/2 in above equation and solving that we get answer

Pi/6 = 0.52

Thank you.