On further inspection, it was found that the mathematician had assumed an ideal sphere of constant radius, while the real object was in fact oblate. The mathematician had neglected to take any measurements, leading to an incorrect value. The physicist's answer was correct, but only at sea level at nominal temperature.
The engineer is currently using calipers to measure the diameter of the object at many different angles in order to build a CAD model. He said we could expect results next year.