Rlwood, did you get the ball's circumference measurement by using a tape, or by a caliper? The difference is very important. Here's why.
As Armor9 indicated, 10-inches Circumference divided by Pi (3.1416) means the diameter is 3.18-inches. BUT, the ball's circumference APPARENTLY was measured with some thick rust-encrustation on it... which means the measurement would be smaller if the rust-encrustation was completely removed.
If that ball was mine, I would use a hammer to knock off the encrustation on two spots exactly 180-degrees opposite from each other, and then use a digital caliper to get the diameter measurement.
Until we get a caliper measurement:
3.18 inches is in the size-range for a Colonial era French 4-Pounder cannonball, and a Colonial era British Navy "Boarding Grenade." But the photos show the ball's walls are too thin to be an explosive cannonball... so I'd have to go with a grenade, UNTIL we get the more-accurate diameter measurement.
Also "meanwhile":
The World War One French Model-1914 ball or rod (rifle) grenade was an 81mm (3.19-inch) cast-iron ball with thin walls, to keep it light enough for achieving good range as a rifle-grenade. So, if your thin-walled ball really does measure 3.18-inch or so, that's what I think you've got.
More info on the French Model-1914 ball or rod grenade is available here, with photos:
French Ball Rod Grenade - Inert-Ord.net
It's understandable that you might ask, how the heck can a World War One French ball-grenade get dug here in the US (Kentucky, apparently). The answer is, various types of French Military Ordnance got tested by US troops here during World War One. Believe it or not, here's a photo of a WW1 French ball-grenade that was dug at Vicksburg's entrenchments. Soldiers like to train in entrenchments, and it didn't matter to them at all that the entrenchments were 55 years old.