Here's some info for you while we wait for the close-up photo (hopefully, more than just one photo).
Based on the ball's precisely measured weight of 3 pounds 9.4 ounces, it is not a cannonball -- because it doesn't match up with any of the data telling historical cannonball diameters and weights. Go here: Cannon bore, shot, and shell diameters for smoothbore guns
The nearest match-up for your ball's weight is a 4-Pounder caliber Solid-Shot cannonball, which was specified to be 3.12 inches in diameter and weigh 4.07 pounds (4 pounds 1 ounce). But your ball is 7 ounces short of that weight.