It has been suggested by Pommerening that the NK change came about related to the oipe replacing the hekat as the Pharaonic volume control unit in official lists.
Hana Vymazalova evaluated the hekat unit in 2002 within the Akhmim Wooden Tablet by showing that five answers were returned to (64/64) when multiplied by the divisors 3, 7, 10, 11 and 13.
The hekat unit was defined, in terms of its volume size, in the Moscow Mathematical Papyrus by MMP #10, by approximating π to around 3.16.
The approximation of π was achieved by squaring a circle, increasingly (i.e. for the denominator in terms of setats: 9, 18, 36, 72, and 81, Gillings, page 141) until the vulgar fraction 256/81 was reached, the only relationship that was used in the Egyptian Middle Kingdom.
However that may be at least a sphere that has a circumference 523.5 millimeters will actually have a metric volume about 2.42269 liters or roughly half of a hekat or about one sixtieth of a royal cubic cubit to two parts in a hundred.