How exactly do you measure circumference or diameter?

As to your assumption that they would never be able to shape it perfectly into a circle, suppose you had a circular block of wood. You cut a piece of paper slightly longer than the circumference, wrapped it around the wood, and drew a line on the paper using the circle as a guideline. Now you measure the length of the line. This would be trickier than it sounds, but it would be possible with the material they had, and would be very accurate.