When you say that the Volume 'pot' has broken off, do you mean that the shaft and knob are missing or that the whole thing has broken off the pcb?
Here is the Ifixit teardown for a Rogue G10.
Repairing the audio amplifier
Unfortunately, I cannot find a wiring diagram for the amp.
Looking at it, the Volume pot is mounted onto the pcb. If it is still there (or remnants of it) hopefully there will be some markings on the case of the pot which will give an indication of its' value and/or type. If there is nothing left of it perhaps there is some marking on the pcb designating the pot which may assist in identification.
In the teardown pictures it physically looks about the same size as the bass and treble controls, so whilst it can obviously have a different resistance value the power rating should be the same e.g. 5W or 10W. It's a bit hard to tell from looking at the pictures.
If you cannot find any other information on it check the number of connections on the board for the pot and then connect a 50K Ohm 10W pot and see how it works. You can always reduce the resistance value if the control is to coarse.
Hopefully this is of some help.