Radius of about 15x 10^9 light-years ?
Well.. such a good question. I think the question here is about "our" Universe ?
I'm not sure what would be the dimension of "volume times mass", maybe were there the question of "volume times (Mass/Volume)" ?
According to the known approximation about the Universe, the majority of the astrophysicists are about to tell that the time (age) of the Universe is about: 15 x 10^9 years.
Well, one thing done.
Now, defining literally the word "Universe", this understand all "that we know"; by this way: also a so light thing as Light/photons.
So for the radius (I am however not meaning here that the Universe would be spheric), as Einstein thought that Light couldn't be overtook (in celerity) - and now the reader guess where this purpose is going - :
the radius of our Universe would be about time x celerity :
(15 x 10^9 years) x (about 300'000 km/s),
and knowing that a year is (365 days x 24 hour/day x 3600 s/hour ), so 31'536'000 s:
this would be about:
(4,7304 x 10^17 s) x c, ("c" for the celerity approximated to 300'000 km/s), so:
1,41912 x 10^23 km,
and "km" seem to be not relevant unity for Universe, so this would re-lead us to the first line above, knowing:
15x 10^9 Light-Years.
About different questions of density of the Universe, I don't know anything, or only that some measures are telling the astrophysicists about "a density around 1", and which one is.. ..critical for the scenarios of possibles evolutions of the Universe (knowing: eternal expansion / regression to a Big Crunch / incredible stagnation in case of a density of exactly "1".
P.S.:
Due to esoteric observations related to the unknown Black Energy, they are most thinking about an accelerated expansion.
N.B.:
A few weeks ago (as the atomic model of Bohr was overtaken in the 20's of 20th century, with the help of Schrödinger and others),
the Light seemed not to be unsurpassable - so in other word: surpassable - here by some neutrinos
(the experiments were repeated in the European Center for Nuclear Research for six months),
it would exist a c' > c,
so the Universe could be even larger.
(But the experiment has to be verified in other laboratories for 3 years since now.)