Identifying what PowerMac I have
The Mac in question is a Power Macintosh G4 800 (QuickSilver 2002) model built in June 2002. In your case, it has the 800 MHz PowerPC 7455 G4 processor (as opposed to the PowerPC 7450 variant). This processor had a single core, but also had what Apple called an AltiVec Velocity Engine. 

The specific model details are: M8493 (EMC 1896) with model identifier PowerMac3,5. 

In your question you mentioned Mac OS 9. This model is only officially capable of booting into Mac OS 9.2.2 (not an earlier version).


You can check your serial number!

Since posting this answer I remembered that everymac.com has a lookup function on their site that allows users to enter a serial number to identify their hardware. You can access this at: http://www.everymac.com/ultimate-mac-lookup/