Exhaust question new 3x6x7 grow room. Filter to hood to fan to Exit?

New to the indoor growing basically. Don't like chances of being caught outdoors, however nothing grows like outdoors (we will see?). Anyway, I have ended up with a free 4c448a dayton shaded pole blower a few years ago and decided to keep it for some reason. Now that I have a good use for it, I have a question as to how to hook up to the rest of my set up before I order my carbon filter which is another question? 1. How big of a carbon filter do need for room(3x6x7) and blower at 465 cfm pulling through a hood too? Again I would like to hook up carbon filter running to hood then hood to fan, fan to blower and blower out. I will be running a 600watt hps for this room. Please advice greatly appreciated.And thank you.