Re: Science Question
The first problem you have with an enclosed air space (submarines, spacecraft) is CO2 buildup. This usually screws you up before oxygen depletion. Life support systems use a "scrubber" that absorbs CO2 with a chemical, and then something else that lets new oxygen into the system. The latter can be oxygen from a tank, or an "oxygen candle."
A ten foot diameter sphere is going to get pretty bad pretty quick.