Question: Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a (averaged over the whole surface of

 Show that the average straight-line distance to a fixed point on

the surface of a sphere of radius a (averaged over the whole

Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a (averaged over the whole surface of the sphere) is 4. [Suggestion: Take the sphere centered at the origin, and choose the "north pole" as the fixed point.]

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