The kit isn't a radio king kit. they were no longer made during this time period. this kit is a 61N classic rock set the 18" floor tom is a 5 ply shell.

Not that it really applies to this kit anyway but Slingerland did market sets under the Radio King name...but only the snare drums had the one ply shell. The others were standard 3 ply.

I bet they sound great!

Looks like a re-lacquer job. The badge has lacquer on top of it. There is a chance the set is a "frankenstein" set. That's when you put together a set out of orphan pieces and then peel them off their original finishes and re-lacquer them to make them match. It is not a Radio King and you shouldn't pay much for it. (About 50% or 60% of what you should pay for a legit set)