Drilling Holes Through Balls and Cubes : Maximizing the Total Exposed Surface Area

Suppose that we are allowed to drill a cylindrical hole of any radius through the center of a unit ball or a unit cube in a given direction. Which radius will maximize the total exposed surface area (ESA) of the finished object? If we are allowed to drill two or three mutually orthogonal cylindrical holes of the same radius, which common radius will maximize the total ESA?