Solution

d = 2160 miles
r = d / 2 = 1080 miles

SA = 4 * PI * r ^ 2 = 4665600 square miles
V  = 4 / 3 * PI * r ^ 3 = 1679616000 cubic miles

Let x = the conversion from lunars to miles
SA * x ^ -2 = V * x ^ -3
     SA * x = V
          x = V / SA = 360

Therefore, there are 360 miles in one lunar

Comments

• We could not find a printed answer, but this QOD was straight math
• I would like to remind readers that mistakes are included for the sake of their existence. No sense in tampering (extensively) with history

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