The packing fraction in SC :-
1 x (4/3) PI (R)3 / (a)3
i.e. 1/1 x 4/3 x PI/1 x [a /2]3 x 1/ (a)3
i.e. PI / 6
i.e. 0.52
The packing fraction in BCC :-
2 x (4/3) PI (R)3 / (a)3
i.e. 2/1 x 4/3 x PI/1 x [(square root of 3) x a /4]3 x 1/ (a)3
i.e. (square root of 3) x (PI / 8)
i.e. 0.68.
The packing fraction in FCC :-
4 x (4/3) PI (R)3 / (a)3
i.e. 4/1 x 4/3 x PI/1 x [(square root of 2) x a /4]3 x 1/ (a)3
i.e. PI / (3 x square root of 2)
i.e. 0.74.
Hence the FCC structure possesses maximum packing density among the three crystal structures SC, BCC and FCC.