## Packing Fraction of Face-Centred Cubic Lattice

**Let ‘r’ be the radius of sphere and ‘a’ be the edge length of the cube**

**As there are 4 sphere in fcc unit cell**

**∴ Volume of four spheres = 4 (4/3 πr**^{3})

**In fcc, the corner spheres are in touch with the face centred sphere. Therefore, face diagonal AD is equal to four times the radius of sphere**

**AC= 4r**

**But from the right angled triangle ACD **

**AC = √AD**^{2} + DC^{2} = √a^{2} + a^{2}= √2a

**4r = √2a**

**or a = 4/√2 r**

**∴ volume of cube = (2/√2 r)**^{3}