Conventional steel wheels like the # AM20514 often fit older trucks like your 1938 GMC pickup. However, these are only rated for trailer use. These 15" wheels have an offset of 0 and a 6 on 5-1/2 bolt pattern. A hubcap will fit but it would be like the # AM981306 which is slightly larger than your 7-1/2" to 8" measurement with a 10-9/16" overall diameter.
If you have a 5 on 4-1/2 bolt pattern then the correct wheel would be the # AM20504. This would use a slightly smaller hubcap like... view full answer...