Calculate rocket centre of mass

I wish to calculate the centre of mass of a two stage rocket, for example the Falcon 9. Since the mass of the rocket is constantly changing (first the mass of the first stage is depleting, then the second stage), how do I go about calculating the instantaneous centre of mass?

I'm assuming each stage consists of a hollow outer cylinder made of say, aluminium, and within it a cylindrical shaped propellant which is constantly being depleted. Then there is a payload at the top in the shape of, for example, a nosecone.

Any help is appreciated!