YOu want to calc Vol.Atoms/Vol.UnitCell The unit cell is a cube. FCC unit cell has an atom in the centre of each face split in half so half of each atom is within the unit cell. 6 sides so 6 x 1/2 = 3 equivalant whole atoms. It also has an atom on each corner split so only an eighth of each is within the unit cell. 8 corners so 8 x 1/8 = 1 equivalant whole atom. IN total thats 4 equivalant whole atoms. Draw a line across one of the faces of the unit cell diagonally from one corner to the other. THis line goes throug the corner atom (centre to outside) then through the face atom, then the other corner atom. It should be noted that the face atom touches each of the four corner atoms on the same unit cell face. If the atoms are the same size then the length of this line is R (corner atom) + 2R (face atom) + R (corner atom) = 4R We will call the unit cell sides 'a'. From geometry we can determine, a^2 + a^2 = (4R)^2 2a^2 = (4R)^2 a = sqrt[16R^2/2] Volume of unit cell = a^3 becuase its a cube a^3 = [sqrt[16R^2/2]]^3 you have 4 whole atoms (equivalant) so volume of 4 atoms = 4 x 4/3 x PI x R^3 = (16.PI.R^3)/3 Packing fraction = Vol.Atoms/Vol.UnitCell = [(16.PI.R^3)/3]/[sqrt[16R^2/2]]^3 Simplify this down and you get 0.74