Density = Mass/Volume.

Mass = volume x Density.

Volume = Mass/Density.

There are 3 cases.

Volume is kept constant.

Density is kept constant.

Mass is kept constant.

First case:volume is kept constant. In this case, density has nothing to do with volume. The density increases with increase in mass and the rate of increase depends on the volume. For Example: Imagine two balloons. Both blown up to the same level(same volume) with one filled with air and the other with water. Obviously the balloon filled with water is heavier and thus more denser( and vice versa).

Second case:Density is kept constant. In this case, volume has nothing to do with density. The volume increases with increase in mass but the rate of increase of volume when mass is added depends on the density. For Example: Imagine a container partially filled with water. When water is added to the already existing water, the density of water still remains same hut the volume has increased. Of course mass of the container after adding water is higher than the mass of the container before adding water.

Third case:Mass is kept constant. In this case, yes, volume is inversely proportional to density. Not much explanation is needed here. For example: Imagine a squeezed sponge and an loosely left sponge(the sponges are identical). Here, volume of the squeezed sponge is less but it is more denser when compared to the free sponge whose volume is more than the squeezed sponge.

Volume is constant and mass isproportional to density. Now if all the cooking gas in the same cylinder is transferred in a lager cylinder, the mass of gas will be the same, but its volume will increase anddensitywill decrease, this is becausedensityis inverselyproportional tovolume.