...leading to an approximate diameter for the tube of 4', not 3' (as the Season 2 setplan shows). I always took the setplans as correct, but the screencaps do not lie!
You're just teasing us, right?
You can get the "diameter" of the opening all the way up to five feet or six feet or any amount of feet you want simply by making the tube even steeper. The actual diameter of the tube is measured perpendicularly to the walls.
Take an empty paper towel roll cardboard core and cut it. But don't just cut it perpendicularly; cut it diagonally, at a really extreme angle--like from almost one end to almost the other end. Then measure from the top of the opening to the bottom of the opening. Abracadabra! You now have a cardboard tube that has become, like, eight inches in "diameter" instead of just an inch and a half!