You raise an interesting point that the area of a circle was of interest which appears to be so from the diameter of the holes in the top ledge of the sarcophagus which are precisely 9/8 digits in diameter so an area of one square digit (by applying the AE formula of 8/9 x diameter and viewing the product as square units).

This is, of course, not the place to debate the matter, but it seems inconceivable to me that the perimeter of the long walls of the King's Chamber just happen to conform to a model of a circle with a diameter of 560 digits (radius 280 digits) with the diameter as the length of the chamber and the perimeter of 1760 digits corresponding to the circumference of the circle bearing in mind Petrie's hypothesis that the height of the Great Pyramid at 280 cubits can be regarded as the radius of a virtual circle with the perimeter of the square base equal to 1760 cubits corresponding to the circumference of the circle.

It doesn't get much simpler than the fact that it would have been easy to measure the circumference of a circle with a diameter of one royal cubit (7 palms) as having a circumference of 22 palms, and if the architect was aware of the the approximate area of a circle from the 8/9 ratio then the idea of measuring the ratio of the circumference to the diameter would have occurred to most with a mathematical inclination.

I agree that there isn't much value in knowing the ratio of the circumference to the diameter of a circle unless someone in Ancient Egypt took the giant step of using that ratio to calculate the area of a circle, an idea that was rejected by Petrie (and rejected by some of those who accept Petrie's 22/7 hypothesis).

The hypothetical sphere with a diameter of 2.5 cubits (70 digits) equal to the internal volume of the sarcophagus has a circle with an area to the internal rectangle which means that the internal depth is 2/3 x the diameter of 70 digits, which it is, most precisely so.

It is obvious that the volume of a sphere was regarded as 2/3 x volume of a cylinder (with a height and diameter equal to the diameter of the sphere).

Archimedes is remembered as having proved that the volume of a sphere has a volume of exactly 2 parts relative to 3 parts for its encapsulating cylinder, so his tombstone had a model of the configuration, but all have overlooked that the same configuration is apparent in Khufu's sarcophagus.

Mark.