A model of the size and pi shape of the Great Pyramid is represented in the design of the King's Chamber on a scale of one digit to one royal cubit, with the royal cubit consisting of 28 digits. The scale model is 1/28:

The long walls of the King's Chamber have a length of 560 digits (20 royal cubits), and there are 5 courses of granite blocks with a height of 320 digits, as 5 x 64 digits.

On this basis the length of the chamber is the diameter of the hypothetical circle, at 560 digits, and the virtual radius of 280 digits corresponds to the height of the pyramid at 280 royal cubits.

These numbers correspond to the pi ratio 22/7, which may have been regarded as exact, because a circle with a diameter of 7 palms has a circumference of 21.99..palms, which might well have appeared to be exactly 22 palms on measurement with a cord.

The division of the royal cubit into 7 palms coupled with the natural division of the palm into 4 digits means that there were 28 digits in the royal cubit. This is apparent from the corbels of the Grand Gallery with 7 overlaps of 1 palm, and the corbels in the Queen's Chamber with 4 overlaps of 7 digits. The division of the cubit by 7 and by 4 means that the royal cubit had 28 divisions as 4 x 7 = 28. This division is found on rulers from later dynasties.

The perimeter of the long walls of the King's Chamber is 1,760 digits (320 + 320 + 560 + 560), which corresponds to the circumference of the hypothetical circle. The length of the chamber at 560 digits corresponds to the diameter of the circle as 22/7 x 560 = 1760 digits.

This design mirrors the pi shape of pyramid on a scale of 1 digit to 1 royal cubit, with the radius of the circle equal to 280 digits:
The perimeter of the base of the pyramid with 4 sides of 440 royal cubits is equal to 1,760 royal cubits as the circumference of a virtual circle, and the design height of the Great Pyramid was 280 royal cubits as the radius of the virtual circle.

Sir W.M.F. Petrie noted that the internal volume of the sarcophagus in the King's Chamber corresponds to that of a sphere with a diameter equal to a quarter of the width of the chamber. The diameter is therefore 2 1/2 royal cubits, which is 70 digits.

We can calculate that the hypothetical volume of the sarcophagus equates to 179,666.66 cubic digits, although, as we shall see, it was not necessary to evaluate big numbers.

The number 64 is represented as 64 digits in each of the courses of the King's Chamber, and we know that the fraction 1/64 was important as the eye of Horus in ancient Egyptian mathematics.

If the sarcophagus was 1/64 of the symbolic model volume then:
64 x 179,666.66 cubic digits = 11,498,666.66 cubic digits.

The scale model of the King's Chamber is on a scale of 1 digit to 1 royal cubit, so the proposed symbolic volume from the model is 11,498,666.66 cubic royal cubits

The triangle in the cross-section of the Great Pyramid has a length of 440 royal cubits as the side-length of the pyramid, and a height of 280 royal cubits.

This triangle is equal to the area of a circle with a diameter equal to the height of the pyramid, which means that we get a picture of a virtual sphere by rotating the circle through 90 degrees from the north-south axis to the east-west axis.

(The volume of a sphere can be imagined as being divided into millions of tiny needle shaped pyramids, such that the height of the pyramids is equal to the radius of the sphere, and the surface area of the bases of the pyramids is equal to the surface area of the sphere. The idea of contemplating a pi shaped pyramid as a sphere commends itself from this picture, as well as from the picture of the equal area circle.)

Hitherto there has been no proof that the Great Pyramid was regarded as a sphere. A sphere with a diameter equal to the height of the Great Pyramid at 280 royal cubits has a volume of 11,498,666.66 cubic royal cubits. This is the symbolic volume represented by the sarcophagus.

The numbers help us see the picture, but the picture is much simpler in fractions, and can be understood from 5 simple observations:

The volume of a sphere was perceived as:
2/3 diameter (depth of sarcophagus) x area of circle (internal area of sarcophagus)

The diameter of the virtual sphere apparent from the design of the sarcophagus is a quarter of the width of the chamber, as noted by Petrie, which is 1/4 x 280 digits (10 royal cubits).

It was an incredible to achieve to construct the King's Chamber out of granite blocks so that the height of each course is 64 digits.

The key to the symbolic volume of the model is 1/4 x 1/4 x 1/4 = 1/64, so the internal volume of the sarcophagus is 1/64 of the volume of a sphere with a diameter equal to 280 digits (10 royal cubits) as the width of the chamber.

The model design of the King's Chamber is on a scale of 1 digit to 1 royal cubit, so the virtual sphere has a diameter of 280 royal cubits as the height of the Great Pyramid.

Mark