because the "volume" of the solar system comes from pluto's trajectory (when it was the last planet), while its mass comes from the Sun...
The last statement is an approximation for the solar system because the mass of the sun is pretty much overpassing the masses of the rest planets. Of course there are pretty massive planets in the solar system as well (eg Jupiter) so it's an approximation.
Also for the case of atoms, of course you can't use the Solar System model, except for getting the idea of it. We know today that the nuclei have a radius of approximately 1 to some hundrends of fm (in the past what people knew was that the nuclei existed in a very small region-condensed- within the atom by Rutherford's experiment)... The average radius of an electron's existence in the atom (the distance in which you are pretty sure up to 99% the electron will exist) is of the order of 1-100 nm ...
So the radius of the atom would be given by the last.
For the case of electrons though, they all have the same mass, but it's still very much lighter than the mass of a proton
(~10- 3~4 orders of magnitude less)
So the protons' masses overwhelm the electron masses, so approximately you can say that the atom's mass is given by the nucleus...
Of course that's not really true- you have to take into account the masses of electrons sometimes (eg in nuclei decays)