Ahhh, I think I know what this object was for. It was an ancient Egyptian
fondue pot.
Sorry, couldn't help myself.
I've spent awhile looking over that
web page to which legionromanes linked us earlier, and it provides some useful information. I am now leaning toward this object being some sort of ritual offering tray.
Here's another look at it.
I can't tell if the center tube is hollow or plugged at the bottom, but it would be ideal for the issuance of incense. Food items could've been piled in the shallow bowl portion. I still can't quite figure out the purpose of the three lobes, but the handles behind them would've been perfect for carrying a nice pile of offerings. One or two priests may have done this.
Being that the owner of Tomb 3111 was buried at Saqqara, he most likely lived and died in that area. The tomb owner, probably named Sabu, was a high-ranking provincial official. He may have been tied in with the temple of Ptah in the administrative capital of Mennefer (Memphis), where such an offering bowl would've been used.
A more mundane explanation is also possible. As I mentioned earlier, the object reminds me of some large stone platters I have seen, although considerably fancier. It's possible this was used for formal banquets, the sort of thing ancient Egyptians enjoyed, in particular the elite individuals. Incense and heaps of food were common at banquets just as they were in temples.
I still have a hard time picturing how this thing would float. I don't think it would, at least for more than a moment or two. I don't see how it would displace water without toppling over and sinking. Even by Dynasty 1 the Egyptians were well versed in constructing all manner of vessels for flotation, and stone was not one of the materials they used, as legionromanes said earlier. I really do think the thing is what it appears to be: some kind of elaborate bowl or platter.
If it looks like a duck, and quacks like a duck...well, you know.