Consider the solid bounded by the three right circular cylinders
*x*^{2} + *y*^{2} = 2*a*^{2} (greenish-yellow),
*x*^{2} + *z*^{2} = 2*a*^{2} (red), and
*y*^{2} + *z*^{2} = 2*a*^{2} (blue) shown in the figure below.
An ant wants to follow the shortest path along the surface from the point (*a*, *a*, 0) to the point (0, *a*, *a*).
What is the length of this path?