If you have a brain mask, how about taking this relation:
V= (4/3) \pi r^3
… and inverting it to get radius:
r= (3V/4\pi)^{1/3}
… and then you just need the physical volume of the mask, which could be got, for example in AFNI:
3dROIstats -quiet -nomeanout -nzvolume -mask DSET_MASK DSET_MASK
? That should be a reasonable approximation.
–pt