Holocaust survivors like this one often describe the Nazi's cutting hair before the gassing began. To me this makes no sense, since they will die regardless. Is there a documented reason for doing this?
Also, the barber describes the room being 12*12, then says over 150 people were packed inside of it. I find it hard to believe over 150 people fit inside a room around this size
Money, dear boy. Hair cas be used for wigs and filling the furniture and car seats. Unlike soap from fat that didn't catch on, proceder of selling shaved hair was well documented. They weren't particulary expensive but profitable giving the sheer amount. Remember that Nazi Germany recycled golden teeth, clothes luggage and even lunches of their victims.
For the room-see the photos and you can stop wondering. When nobody cares about well being it's really possible to gather crowd like this.
For more details see excellent book and BBC series "Aushwitz. Nazi and Final Solution" by Laurence Rees.