>>12054591based on the wiki apparently saying method of exhaustion
They probably imagined filling a cone with height H with several cylinders of height H/n, and variable R. Then they would figure out the volume of all those cylinders.
Then they would fit a cone within several cylinders of H/n, with a variable R again. Then count the volume of these cylinders.
The volume of the cylinders inside the cone and the volume of the cylinders which contain the cone would provide boundaries.
It's somewhat like the trapezium method for figuring out the area under the curve. Or almost exactly like figuring out the circumference of a circle.
Take circle of radius 1.
Make a small square with each corner touching the circle, within the circle.
Make a big square, with each side touching the circle at the midpoint of the side.
Perimeter of the big square > perimeter of the circle > perimeter of the small square
Now you can do a little calculation to produce a big and a small octagon, then a big and small 16-gon, then 32-gon and so on.
In the cone case, you increase the number of cylinders you use to fill up the cone. And you increase the number of cylinders used to contain the cone. As the height of the cylinders gets smaller, you get a better approximation of the two boundaries
