Devldog,Cagedfalcon, what you have here appears to be a cannonball. The whole in the top would have been where the fuse once was. It's hard to see, but there doesn't appear to be any threads on the Inner circumference of the whole. If there were threads, this ball would most likely have had a brass threaded time fuse. No threads indicates that this probably would have had a wooden fuse at one time. This would also most likely make this a Confetrit' (Confederate) artillery fragmentation shell. By the looks, it appears to be a 12 pounder. I have one like yours that I found back in the 80's. Congrat's on a nice shell.
ThecannonballguyIt "appears" to be a cannonball... a version sometimes called a roundshell. The precisely-measured diameter (4.40-inches) and precise weight (7.8 pounds) you reported match up almost exactly with a civil war Confederate Pentagonal "Polygonal Cavity" roundshell. (That is the Ordnance Department's name for what Devldog said.)
But for certainty of ID, I need a few more details. What is the diameter of the fuzehole?
I'm asking because the civil war Ordnance Department's prescribed diameter for a 12-Pounder caliber cannonball was 4.52-inches. You said this ball measures 4.40-inches... which is much closer to a RevWar era 12-Pounder cannonball's 4.42-to-4.44-inches than the civil war era specification of 4.52-inches.
How was this ball measured? With a Pi Tape (a Diameter-Tape), or with a Caliper? Or some other way? In my experience, using a caliper gives the most accurate results... especially if you use it to measure across the ball in more than one direction. (You measure the ball, then rotate it a bit and measure again, then rotate the ball again and measure again, etc.)
A 12-Pounder CS Polygonal Cavity roundshell's "wooden-type" fuzehole is typically about 7/8th-inch in diameter at its top... and the fuzehole is slightly tapered (cork-shaped). The RevWar 12-Pounder fuzehole is larger, and not as deep, and is not tapered.