Milo, the arithmetical 'body' of a problem in the RMP is not enough for me, I need a 'soul' that brings a calculation to life, and I find it by playing with the given numbers.
RPM 56, 57, 58 and 59 concern pyramids. Three of them have the sekad 5 palms 1 finger. A pyramid of this sekad involves a 'sacred triangle': half base 3a, height 4a, slope 5a. I call such a pyramid a 'sacred pyramid'.
The sacred pyramid of RMP 59 has a base of 12 royal cubits and a height of 8 royal cubits. The slope measures 10 royal cubits, and the radius of the inscribed sphere 3 royal cubits. The diameter of the inscribed sphere measures 6 royal cubits, the same as half the base.
Now picture a wooden model of this pyramid: base 12 fingers (22.5 cm), height 8 fingers (15 cm), slope 10 fingers (18.75 cm). Calculate the surface of the model. You'll get 144 plus 60 plus 60 plus 60 plus 60 square fingers, all in all 384 square fingers. Calculate the volume of the model. You'll get 384 cubic fingers ...
For a next step you may transform the volume of this pyramid into a sphere. It will have a diameter of practically 9 fingers. This leads to a nice expansion of the well known formula for the calculation of the area of a circle into three dimensions:
A square of the side 8 and a circle of the diameter 9 have practically the same area; a sacred pyramid of the height 8 and a sphere of the diameter 9 have practically the same volume (implicit value for pi in both cases 256/81).