Wow you guys, thanks for pointing out this error in the theory. According to my ephemeris, he sun's current apparent size is 1888 arc seconds, or 0.0091533 radians -- about half a degree of arc. The ratio of the sun's radius to its distance from us is the tangent of half that angle, or, in this case, 0.0045767.
In other words, if the sun is 3000 miles away its radius must be 13.370 miles, i.e. it's diameter is 26.740 miles (not 32). If however its diameter is 32 miles (radius 16), then it must be 3496 miles away.
We should have been more precise.