Bottle Holder Problem Idea

Last weekend I had the privilege of having dinner with my grandparents. While I was there, my grandma showed me a gift she received on the form of this wine bottle holder. Upon seeing it, I instantly thought of a number of questions. 

 

1) What is the angle of the base of the holder? 

2) At what angle is the bottle in relation to the holder? 

3) Are those angles the same? 

4) Is there a way to prove the angle congruence?

5) If the bottle angle is equal to the angle of the base is that a requirement for the holder to work?

6) At what level of liquid will the bottle fail to stay up? 

7) Would it be possible to dispense liquid from the bottle while it is in the holder? If so, for how long? 

These are all questions that my family and I brought up during dinner, and I think it would be interesting for students to think about these questions and formulate a way to answer them. 

What questions would you ask, and do you know the answers to any of the ones above?