Okay, lemme do this for Upriver:
Radius of the sun: 7 108 m
Mass of the sun: 2 1030 kg
Average density: 1410 kg m-3
Density of iron: 8 103 kg m-3
So we take a shell of iron of thickness D and calculate how heavy it is.
Volume is 4 pi R2 D (when the thickness is much smaller than the radius of the Sun).
V = 4 pi R2 D = 6 1018 D m[sup3[/sup] = A D
Knowing the density of iron and the volume with parameter D and the mass of the Sun we can get an estimate of how thick the iron layer can be:
D = M / A*Fe = 2 1030 / 6 1018 * 8 103 = 41 106 m
Well, here we see that the iron shell in the Sun is only 6% of the radius of the Sun.
I assume that the inside of the shell is filled with cheese :-)