Problem #11
The interior dimensions of a rectangular box with a lid on it are 3 feet by
4 feet by 5 feet. A post in the form of a right circular cylinder 1 foot
in diameter just fits diagonally in the box, touching all six inner faces.
How long is the post? [A numerical approximation to 5 decimal places will
suffice.]
[This can be interpreted as a three-dimensional generalization
of last week's problem]