It depends on the field piece and type projectile.
The following is the closest to a 9 lb. projectile that I can find:
12 lb. howitzer ......8.90 lb. round ball...4.62" bore
10 lb. Parrot rifle...9.50 lb. shell........3.00" bore
Ordinance rifle.......9.50 lb. shell........3.00" bore
12 lb. Blakeley ......10.00 lb. shell........3.40" bore
12 lb. Whitworth......12.00 lb. shell........2.75" bore

Your ball is probably for the 12-lb howitzer with a 4.62" bore and 8.90" lb. round ball. The nominal bore size that will accept a 9 lb. cast iron ball is 4.187" diameter.

The muzzle loading shells for cannons with rifled bores weigh more in relation to the bore size than the smoothbore cannons that fireed round balls because the shells are elongated explosive projectiles. The 12 lb. Whitworth was the first breech loading rifled cannon with a range of 2,800 yards at 3 degrees elevation. A a cannon that fired a solid 12 lb. round ball would have a nominal bore size of 4.625". The 12 lb. howitzer shown above that fired an fused explosive hollow round ball filled with black powder weighed only 8.90 lb.