As Taz42o indicated, super-precise measuring of a ball's weight in combination with its pecisely-measured diameter will tell you whether it is a solid ball or a hollow ball.
www.civilwarartillery.com/shottables.htm
A typical Civil War era "12-Pounder Caliber" Solid Shot cannonball (whose diameter is about 4.52-inches) weighs just a bit over 12 pounds, and the hollow explosive shell version weighs from 7 pounds to 10 pounds, depending on whether or not it has antipersonnel balls inside it.
As Taz42o mentioned, a Civil War era "12-Pounder Caliber" Solid Shot cannonball's officially-specified diameter was 4.52-inches and 12.25 pounds (12 pounds 4 ounces). However, that weight is is for top quality Government Arsenal made ones weighed. Cannonballs made by less-skilled workers at privately owned foundries often contained internal casting-flaw bubbles in the iron, which caused the ball to weigh a few ounces less than it ought to.
Also, Revolutionary War era cannonballs were a few hundredths of an inch smaller in diameter than Civil War era ones. Therefore, the Rev War cannonballs will weigh a bit less than the Civil War ones listed in the 1861 Ordnance manual's "Shot Tables" charts.
I've seen some Rev War solid-shot cannonballs which have a circular depression similar to what is seen in your photo of Delaware River battlesite ball. But the depression in that ball looks larger than any I've previously seen. It looks more like a Civil War era Bormann-fuzed cannonball whose fuze is missing. Please tell us the circular depression's diameter and depth.
To authenticate that ball as a cannonball, you'll need to use a Caliper or a Diameter-Tape to precisely measure its diameter, and a Postal Shipping Scale to precisely measure its weight (in pounds and ounces.). A typical household bathroom weighing-scale is too inaccurate. For info and instructions, please read the article I co-wrote, here:
SolidShotEssentialsMod
When you've done the precise diameter and weight measurements, please post them.
Meanwhile... you asked if that ball is dangerous. There seems to be no evidence at all that an EXCAVATED cannonball has ever exploded just from being dropped -- or even from being hammered-on. For example, we relic-diggers have excavated multi-thousands of cannonballs... and not even one of them has exploded from being hit with the shovel during the digging-up process. So, even if it is an explosive cannonball, it is not dangerous to handle. Just don't drill into it, or put it into a fire (or oven).
