A cup of coffee contains approximately 100 mg of caffeine. When you drink the coffee, the caffeine is absorbed into the bloodstream and eventually
metabolized by the body. The caffeine is absorbed at a rate of 13 % an
hour

This is an optimization calculus problem where you would need to know a little bit more about the box, atleast i would think. You would just need to use the volume equation of a sphere as the restrictive equation in the optimization problem. Perhaps there is a way to solve with the given information, but i do not know how to.