Volume - important physical characteristic of a three-dimensional figure. Traditionally in mathematics use integrals for finding of volume of figures. In a case with a cone it is possible to manage easier way, to clear school students.
Instruction
1. For a start we will remember Cavalieri's principle. This principle claims that if two volume figures it is possible to arrange so that at section their parallel planes flat figures of the identical area, then these three-dimensional figures of equal volume turned out.
2. Let's consider a pyramid of the same height and area of the basis, as a cone. Let's cut a cone and this pyramid one plane. In the section of a cone there will be a circle, in pyramid section - a triangle. At the same time in section them on the basis we will receive flat figures of the equal area. Then for these volume figures Cavalieri's principle works, so the same volume, as a pyramid has a cone.
3. For a triangular pyramid the following formula of calculation of volume is fair: V = S*h/3 where S is the area of the basis, and h is pyramid height.
4. Then for a cone the formula is also fair: V = S*h/3. At the same time it is easy to express the area of the basis of a cone through radius: S = πR². Then cone volume: V = S = πR²h/3.