The French had pretty much the same cast-iron sphere filled with 110 grams of black powder from 1847 until the outbreak of WWI... Probably close to the naval grenades thrown aboard enemy vessels or at hostile boarding parties...
The grenade was standardized in France by Gribeauval in 1777 under the shape of a 9.5 cm diameter pig iron hollow sphere drilled with a smooth hole for the insertion of a wood plug with a wick inside ('fuze').
U.S. Navy grenades seem rather similar... I used to have an image of the copy of the Ketchum type grenade with the paper streamer tail instead of the wood dart-like projection with the tail fins... Also, descriptions of sieges indicate a lot of "spherical case shot" was repurposed as huge hand grenades.
According to Phil Collins, The Alamo and Beyond: A Collector's Journey (Buffalo Gap, TX: State House Press, 2012), pp. 268-9:
"By the Mexican War, however, hand grenades appear in great abundance in Mexican army stores. For instance, among the relics from the [May] 1846 Palo Alto battlefield was 'a small shell, or hand grenade of brass, and hollow of course' ... At the capture of the castle of Perote, Mexico, the U.S. army found "fourteen thousand three hundred bombs and hand grenades; ... "
Assertions and claims are made that these could be variously thrown by hand after ignition of the fuse, rolling them down "an embankment upon assaulters,' or lobbing them singly or in groups from small mortars or howitzers. Also, a rock sling, or a staff sling could be used to aid in lobbing the things. Apparently a French officer, the Marquis Joseph de Valliere attached a three-foot cord to French grenades to assist in longer--and perhaps more accurate?--throws.
Many U.S. Civil War officers were veterans of the Mexican War, so perhaps some of their experiences with such "infernal machines" made its way into Civil War trenches, rifle pits and redans/ redoubts / field fortifications / sieges?