Many types of galaxies are nearly flat - all stars are approximately orbiting the center of the galaxy in the same plane. Still, that would mean that the "volum

Many types of galaxies are nearly flat - all stars are approximately orbiting the center of the galaxy in the same plane. Still, that would mean that the "volume" (essentially the area of the disk) is on the order of one millionth the size of the Milky Way if the diamater is one thousandth. Of course, it's possible that this galaxy is spherical, so your original numbers apply.