
Re: Ariadne's thread
Posted:
Dec 29, 2011 4:02 AM


RMP 41
A granary in the form of a cylinder has an inner diameter of 9 royal cubits and an inner height of 10 royal cubits.
A square of the side 8 rc and a circle of the diameter 9 rc have about the same area. So the floor of the granary measures about 64 square cubits. Multiply this area by the height 10 royal cubits and you will obtain a volume of 640 cubic cubits = 960 khar = 4,800 quadruple hekat = 19,200 hekat.
Now let us calculate the volume of the granary more exactly:
diameter 9 royal cubits or 63 palms or 252 fingers height 10 royal cubits or 70 palms or 280 fingers
By using the value '7 of 22 for pi we obtain:
diameter 63 palms or 252 fingers circumference 198 palms or 1386 fingers area wall 13,860 square palms area floor 49,896 square fingers volume 13,970,880 cubic fingers or about 636 cubic cubits
A better result than the first one. Now, as a game for advanced learners, we may exchange the numbers:
diameter 10 royal cubits or 70 palms or 280 fingers height 9 royal cubits or 63 palms or 252 fingers circumference 220 palms or 880 fingers area wall 13,860 square palms area floor 3,850 square palms or 61,600 square fingers volume 15,523,200 cubic fingers or about 707 cubic cubits
The walls of the two cylinders have the same area while their volumes maintain the ratio 9 to 10.
The diameter of another cylinder measures 15 royal cubits and the height 6 royal cubits. The wall again has the same area while the volume increases to 23,284,800 cubic fingers or about 1061 cubic cubits.
A further cylinder may have a diameter of 90 royal cubits and a height of 1 royal cubit. The area of the wall would again be the same while the volume would increase to about 6364 cubic cubits.
Now please consider a sequence of cylinders:
diameter 1 2 3 5 6 9 10 15 18 30 45 90 rc height 90 45 30 18 15 10 9 6 5 3 2 1 rc
The walls have the same area while the volume increases in a peculiar way: divide the height by any number and the volume will increase by the same factor ... The lower the cylinder the bigger the volume. And if the wall has no height at all? In that case the volume would be infinitely huge ... A pretty paradox to be discussed in the seminary of professor Ahmes.

