So I was at a family member's house yesterday, and she showed me this heavy ball that belonged to her father. She told me it was made out of ivory, and it was pretty old.

To me it looked more like a ball of petrified wood. She isn't sure what it is made of.

So today I was siting here, coding, and it crossed my mind that I could place the ball inside a water jar, and see how much volume it displaced, and then weight it in an ordinary kitchen scale.

Using both measurements, I could get its approximate density, no?

But I would also need a density table to find its nearest material, where could I find one?

Do you guys think my approach is sound?

Well, you'd have to watch out for things like the center being hollow or a different material, which would result in a density that doesn't apply to any of the materials. If you're relatively confident that it is homogeneous, though, I see no reason why that wouldn't work.

Less messy but perhaps also less fun: find its circumference with a tape measure and calculate its volume?

It isn't a perfect sphere Wan. It's a spheroid, a bit oblong on one of its axis. It also a scaly texture, compatible with Ivory I guess, but also with some types of wood.

My guess is that water displacement would yield the most exact measurement.

Put it inside a MRI and see if it has ancient technology hidden inside.

Ah no, in that case it would not be the easiest solution.
I'm intrigued: you have no idea what it could be?

The water approach will give a closer approximation of the volume, but not so much closer to justify the extra hassle. I don't suppose you have access to a graduated cylinder or other laboratory equipment? If all you've got is kitchen equipment, the tape measure approach will likely provide the closer approximation - even with the oblong distortion and ridged surface.

Most density charts use g/cm3. It's easy to find them for the elements (List of elements by density). Not so easy to find them for compounds. Densities for a variety of wood types can be found at the bottom of this page: Density Tables.

My suggestion is to weigh the object (to the nearest 0.1 gram). Then find the circumference (in cm) and use some math to calculate the volume (V = (c*c*c)/6*pi*pi). Then calculate the density (g/cm3). Then plug that into google along with the word "density" and see what results turn up.

The problem with densities is that the known values are approximative, too. E.g. the density of ivory is given in the range 1,7...1,85 g/cm3, sometimes even up to 1.95 g/cm3 (dependend on the animal species; ivory of a mammoth is even higher). Fortunately, the density of petrified wood seems distant enough to be distinguished: I've found a value of 2.6 g/cm3.

Another way would be to use the hardness of the material. E.g. ivory is soft enough for carving, while petrified wood is not. However, I think you'll loose your head if you start to investigate the object in a destructive manner ;)

Just a guess, but I imagine burning ivory would smell like burning hair (or other proteins). Stabbing it with a hot pin ought to make enough of a smell that it might give you a better guess.

That, or you could post pictures of it for us all to guess.

Maybe it's a 'float' for fishing nets? I have a few of them, about 6" diameter, made of colored glass. You tie the nets to them, and the nets sink beneath the waves, but the top of the net, tied to the floats, well, float. And you somehow catch fish that way, I guess. (See: Drift net - look at the illustration on that page, and notice the orbs holding the net up)

It might not be ivory, but whale bone (See: Scrimshaw), which would make sense, if it actually is a net float.

Post a pic if you can, for curiosity's sake?