A cone has a bottom surface, a side surface, a vertex, a height, and countless generatrixes. The development diagram of the bottom surface is a circle, and the development diagram of the side surface is a fan.
The volume of a cone is equivalent to 1/3 the volume of a cylinder with an outline. According to the cylindrical volume formula V = SH (V = π r? H), and the formula of cone volume is obtained.
Extended data
Properties of cone
(1) Properties of the section circle parallel to the bottom surface: the ratio of the area of the section circle to the area of the bottom surface is equal to the square ratio of the distance from the vertex to the section and the distance from the vertex to the bottom surface.
(2) The cross section passing through the apex of the cone and intersecting with its bottom surface is an isosceles triangle composed of two generatrixes and chords of the bottom circle.
(3) The generatrix L, the height H and the radius of the base circle of the cone form a diameter triangle, and the calculation problem of the cone generally boils down to solving this right triangle, especially the relationship l2=h2+R2.