An authalic radius is the radius of a hypothetical perfect sphere which has the same surface ______ as the reference _______.

• A. Volume, ellipsoid
• B. Area, geoid
• C. Volume, geoid
• D. Area, ellipsoid

Answer: (D)

Authalic means equal surface area. The idea is to find a sphere whose surface area matches that of the reference surface used to model Earth. In geodesy, that reference surface is the ellipsoid, not the geoid. So the defining property is matching surface area, not volume, and using the ellipsoid as the reference. Therefore the sphere’s radius—the authalic radius—is found by equating the sphere’s surface area to the ellipsoid’s surface area. That’s why the correct pairing is area and the ellipsoid.