Re: -_238th book of science for AP // Proving the Principle of Maximum
From Archimedes Plutonium@21:1/5 to All on Fri May 5 21:47:49 2023
Now I have restricted the torus donut hole diameter to be exactly that of pi times the diameter of torus cross section. So I am guessing this restriction causes the ratio of Torus volume and Torus surface area to be the same constant no matter how large
or small the torus is.
So the Volume of my 10 by 10 by 2 torus is (2 x 64) = 128 cubic blocks
The Surface area of my 10 by 10 by 2 torus is 64 block faces on top and 64 block faces on bottom. There are 80 block faces on outer side. There are 48 block faces on inner side. So 64 + 64 + 80 + 48 = 256 square block faces. The ratio of Surface Area/
Volume is 256/128 = 2.
Simple answer, and that this ratio is the same from the smallest torus to the largest at infinity, all because the restriction that the donut hole diameter by 3.14159.. times the cross section of torus diameter.