[Temeraire]

I'm having some issues with this question, I'm not sure if I calculated the packing efficiency right.
Here's the question:

You find a new element. You determine from X-ray diffraction studies that the edge of the unit cell is 7.024 × 10^-8 cm. You also find that this is a very unusual unit cell. It contains a total of 5 atoms and the edge of the unit cell is equal to 4 radii. The molar mass of this new element is found to be 270.06 g/mole. What is the density of this material and what is the “packing efficiency” of this unit cell?

Here's what I did to find the packing efficiency:

1) Total volume of cell: (7.024e-8cm)^3=3.465e-22cm^3

2) Length or radius: 4r=7.024e-8cm, r=1.756e-8m

3) Volume of atoms in cell: (4/3)(3.14)(1.756e-8m)^3(5)= 1.134e-22cm^3

4) Packing efficiency:[(Volume of atoms)/(Total volume of cell)](100)= [(1.134e-22cm^3)/(3.465e-22^3)](100)= 32.73%

Any advice is appreciated, conformation on the packing efficiency would be especially helpful. Thanks!

[UG]

Your working looks correct. I assume the unit cell is cubic shaped?

[Temeraire]

yes it is cubic shaped

[AWK]

2) Length or radius: 4r=7.024e-8cm, r=1.756e-8m

You are freely exchange units! - cm to m

Moreover this is imposible to have 5 molecules in cubic cell. It breaks rules of symmetry in this crystallographic system. In this system cells can contain 1, 2, 4 or some multiplicities of 4 atoms of one type.