Your formula is correct and your density for steel is close (490 lb/cu ft, I use 475 lb/cu ft; precise alloy determines true density) but I calculate about 260 lbs. In any event, a lot heavier than 102 lbs. If it actually weighs 102 lbs and is 10" dia and 12" long, there is something fishy going on, or it is aluminum which is not appropriate for artillery.
New 1020 hot rolled mild steel is running from $1/lb to $1.50/lb. Used (surplus, really) is about $0.40/lb. $0.40 times 260 = a little over $100. Shipping is expensive so having it delivered or at least at hand is worth something. Also, knowing what alloy it is is worth something, too.
Not sure what a piece of 10" dia would be best for. A full size Coehorn is only 8.65" in diameter and a full scale 8" M1861 siege mortar is 16" in dia, so a large but underscale (62%) siege mortar sounds like the best fit, although 12" is a little short. Now what is 5" in diameter that could be used as shot?