From the Albuquerque Journal sky watch:

The “box” of Orion covers about 130 square degrees. The bowl of the Big Dipper holds about 45 square degrees. Crux, the Southern Cross, covers an area of only about 12 square degrees. But what is the area, in square degrees of the entire night sky? 41,253 square degrees.

This implies a set distance out from the surface of the globe to calc – come in closer, fewer square degrees, go out farther, more square degrees – spheres inside of spheres inside of spheres, which one do they pick? Should be able to calc the radius from the formula for the surface of a sphere (strictly, inner surface, but same calculation).