Should the # of atoms in a unit cell be considered to find the % volume change?

[catlip]

Homework Statement

Iron (Fe) undergoes an allotropic transformation at 912°C: upon heating from a BCC (α phase) to an FCC (γ phase). Accompanying this transformation is a change in the atomic radius of Fe—from RBCC = 0.12584 nm to RFCC = 0.12894 nm—and, in addition, a change in density (and volume). Compute the percentage volume change associated with this reaction. Indicate a decreasing volume by a negative number.

Relevant Equations

V=a^3

First of all, I don't think the question was clear enough. Therefore, I had to assume they are referring to the volume of the unit cell.
V=a^3, side length a
aBCC=2R√2, aFCC=4√3/3R
%change=(VFCC-VBCC)/VBCC
I thought this was right until I checked with others who did this:

so the only difference is including the number of atoms per unit cell (4 and 2). But wouldn't this actually be the %change in density?

 

[mjc123]

The question is written a little loosely, but it clearly means the change in volume for the same amount of iron (whether expressed as moles or mass or, as above, volume per atom). This is not the same as the difference in the volume of the unit cell, because the unit cell contains a different number of atoms for the two structures. Density is inversely proportional to volume, so the density increases by (approximately) 1.18%.