Will 400w HPS/MH fit in 4" DIY Cool Tube?

I plan on building one of the DIY Bake A Round Cool Tubes but I was unsure if the 400w bulbs will fit. The tube is only 4 inches and I can't find the measurements for the bulbs. Also, these cool tubes can be wired to work with digital e ballasts correct? Thanks

How do you plan on building it? Make sure it is PYREX or it could shatter from getting too hot. And no 4 inches is not long enough, im not sure exactly but my 400w hps is probably around 8-10 inchs long. Cool tubes dont have power so how would it need to be wired to the ballast? Its just a tube with a fan on one or two ends and some ducting to remove the air from the grow room/cabinet.

I was a lil vague. I meant 4" wide and the Bake A Round is made of pyrex and like 12" long or so. I'm concerned with width not length. The question about the ballast was just me being stupid and wanting to make sure I'll be able to wire the bulb socket to it. While I'm on the topic, I'm going to use this in a gutted clothes dresser with ducting on both sides of the tube. I'll put an exhaust on the left duct with the right duct drawing from outside the dresser. Then as far as cab circulation I'll just use an intake at the bottom of the cab with another exhaust underneath the cool tube exhaust. Should I still be worried about heat? Is 250w a better idea. I plan on hosting 3-4 ladies.