Pressure in bottle - Finding depth

[kriegera]

Homework Statement

A bottle, full of air at atmospheric pressure, whose volume is 500 cubic centimeters, is sunken mouth downwards below the surface of a pond. How far must it be sunk for 100 cubic centimeters of water to run up into the bottle?

Homework Equations

The Attempt at a Solution

The only things i know are that the pressure at the level of the bottle opening must be the same inside and outside. But I'm not sure how to find the depth needed.

 

[ehild]

I hope the attached picture helps. Determine the pressure outside and inside of the bottle at the level of opening. Apply the formula for hydrostatic pressure of water and Boyle's law to get the air pressure inside the bottle.

ehild