chemistry

This problem is from my chemistry book and I am having a little trouble with the intermediary steps:

Barium metal crystallizes in a body- centered cubic lattice (atoms at lattice points only)
The unit cell edge length is 502 pm, and the density of the metal if 3.5g/cm^3. (molar mass Ba= 137.327)
Calculate Avogadros Number.
(Hint: first calc the vol. occupied by 1 mol of Barium atoms in the unit cell, then calc the volume occupied by one Ba atom in the unit cell. Assume that 68% of unit cell is occupied by Ba atoms)

I know that V=edge length cubed (must convert from pm to cm), that there are two total spheres in a bcc unit cell and that Volume= mass/density. Im assuming the volume of 1 mole of Barium is 68% of the total volume, but how do I calc the volume occupied by 1 atom if i am trying to solve for Avogadros number?

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  1. The edge length is 502 pm (convert to cm), then a*(3)1/2 = 4r where r is the radius of the atom. The volume of the atom is V = (4/3)*pi*r3

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