I would be careful of using 22/7 and sphere as an explanation for the design of the sarcophagus.
This sarcophagus is by no means a fine piece of work, as Petrie points out it is not finely wrought and couldn't rival Khafre's. It would be nice to see a study done on the exceptional sarcophagi at Lahun.
Looking at Smyths tables we can have a difference in external lengths of up to 1.5 inches, and width 0.7. Likewise internal lengths diff by 0.56 and breadth 0.71.
Height internal and external are good tolerances as we should expect, as care has to be taken in this area for the sliding lid.
Only the east side of the sarcophagus has a good plane under 0.02, with the other sides quite concave from 0.3 to 0.5 inches.
In my early days of engineering when creating a similar shape (thankfully smaller) out of metal, we always created a master side first, this was made as flat as possible, with all subsequent measures referenced to this side. This basic engineering principle was probably used by the creators of khufu's box, which is why the east side is so flat, compared to the other's.
You seem to suggest that the concave sides were done diliberately; which l doubt. Petrie even describes the errors , for example "the saw was run too deep into the granite, and was backed out again by the masons; but this fresh start they made was still too deep, and two inches lower they backed out a second time, having altogether cut out more than 1/10 inch deeper than they intended."

In short the box is poor quality and so it is not really possible to ascribe any definitive solution to what was intended.
It could be as simple as internal volume being created to reflect half the volume of the solid box, with the sides, bottom, lid having simple fractional relationships to the box. The lid could be 1/7th, the bottom, 1/6th of solid box (or 1/3rd of hollowed out box, leaving the walls and ends as 2/3rds). The volume of the solid box may have been intended to be 500 hekat or 5000 hin, with the removed material being 250 hekat. The above scheme might be possible, but the variability of dimensions presented by the box means that it can only be a theory, nothing can be proved; short of finding a papyrus with the designers blue prints.