The Glass

You have a perfectly cylindrical glass completely full of water (no rounded edges on the bottom, same diameter all the way down).  How do you empty out exactly half of the water?  There are no markings on the glass and you have nothing else to work with.

2 Ant Riddles

1. An ant is on the corner of the floor of a perfectly cubic empty room and wants to get to the farthest corner of the room, on the ceiling.  What is the shortest route?
2. Four ants are on each corner of a square, 2x2" Post-It note.  Each ant is facing the ant immediately to his left.  All four ants begin marching at once, each aiming for the ant immediately to his left.  Eventually the four ants spiral into the middle of the Post-It note, where they meet.  How far does each ant travel?