It "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.