Ckgene, you asked for my analysis of your find, so here it is.
No, definitely not a cannonball -- for several reasons:
1- All cannonballs which were smaller than 3 inches in diameter were "Solid-Shot" -- meaning, not hollow, and therefore, non-explosive.
2a- The wall-thickness of your find is much thinner than any explosive cannonball's wall thickness.
2b- There was a 2.5"-diameter civil war Confederate hand-grenade (which isn't a cannon projectile), but the wall-thickness on your ball is too thin to be the grenade.
3- Your ball does not have the look of excavated iron. (Especially when compared with the obvious excavated iron in the other photo.) All explosive cannonballs were made of cast-iron. Does a magnet stick to the ruptured ball?