Let ‘a’ be the edge length of the unit cell and r be the radius of sphere.
As sphere are touching each other
Therefore a = 2r
No. of spheres per unit cell = 1/8 × 8 = 1
Volume of the sphere = 4/3 πr3
Volume of the cube = a3= (2r)3 = 8r3
∴ Fraction of the space occupied = 1/3πr3 / 8r3 = 0.524
∴ % occupied = 52.4 %