Volumetric and surfaces of bodies of revolution. Cylinder

A given body has volume V if there exist simple bodies containing it and simple bodies contained in it with volumes that differ slightly from V.



Find the volume of the cylinder with a base radius R and height H.
We construct two straight prisms with height H such that the base of one prism is an n-gon containing a circle, and the base of the second prism is an n-gon contained in a circle. Then the first prism contains a cylinder, and the second prism is contained in the cylinder. With an unlimited increase in n, the areas of polygons approach the area of ​​the circle S (the base of the cylinder) and, consequently, their volumes approach unlimitedly towards SH. Then



The volume of the cylinder is equal to the product of the base area and height.