Answer:-

Step 1 : Radius of sphere : In simple cubic lattice, the atoms (spheres) are present at eight corners and in contact along the edge in the unit cell.
If ‘a’ is the edge length of the unit cell and ‘r’ is the radius of the atom, then
a = 2r or r = a/2

Step 2 : Volume of sphere :
Volume of one particle = 4π3 × r³
= 4π3 × (a/2)³ = πa36

Step 3 : Total volume of particles : Since the unit cell contains one particle. Volume occupied by one particle in unit cell = πa36

Step 4 : Packing efficiency :
Packing efficiency