Futhermore, you can remove hidden faces from the tube in various ways. Your method is probably one of the fastest, but there is a faster way even: select the top and bottom Faces and Control/Option+Click the segments (not the connecting Edges) and Group them, Hide the Group. Triple-Click the geometry (which sits in the same position) and Erase it. Bring up Hidden Geometry (powerusers have a shortcut key for this) and UnHide the Group. Explode the Group.
This may seem as more steps but believe me it will speed things up even more.
Alternatively you can select the to-be-Erased Faces and then Group the selected Faces and Erase the group, as demonstrated in this video (skim the timeline to about 80% into the movie).
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Holey Toledo Coen! That is the single most useful tip I've gotten. It has knocked the current #1 off it's perch - eraser+crl+click.
Am I a power user yet?