The figure exhibits how to calculate the amount of space used by the atoms in a single cubic structure.
(a) What is the volume of the entire cube?
(b) What is the volume of one sphere?
(c) What fraction of any one sphere sticks into the cube rather than outside it?
(d) Given that there are eight spheres in all, how much space will they take up in the cube ?

Explanation

(a) Let the ratius of the sphere = a
Edge length = 2a
Volume of the entire cube = `(2a)^(3)=8a^(3)`
(b) Volume of one sphere `=(4)/(3)pia^(3)`
(c) Each sphere at the corner is shared by eight cubes. Hence the fraction of any sphere sticking to the cube `=(1)/(8)`
(d) Space occupied by all the spheres in the cube `=8xx(1)/(8)xx((4)/(3)pia^(3))=(4)/(3)pia^(3)`