Final answer:
FCC and CCP both have structures where atoms occupy 74% of the volume and each atom contacts twelve others, leading to the same packing density. Differences in names do not affect the actual spatial arrangement, which is identical for both structures.
Step-by-step explanation:
Both FCC (face-centered cubic) and FCP (cubic closest packing) structures have the same packing density because they are equivalent arrangements of atoms closely packed together. In both arrangements, atoms occupy 74% of the volume, forming a cubic structure with each atom touching 12 near neighbors. In the FCC arrangement, there are three repeating layers of hexagonally arranged atoms, while in the FCP arrangement, there are two repeating layers of triangularly arranged atoms. The fact that FCC and FCP arrangements have the same packing density is due to their similar arrangement and close coordination number of the atoms.