In a school course of stereometry the concept a cube is entered. A cube or the correct hexahedron is called the convex polyhedron which consists of six sides, each of which is a square. There is a set of geometrical sizes which can be calculated for a cube, one of them is volume. The cube is a most symmetric regular polyhedron therefore calculation of its volume requires the minimum quantity of data.
Instruction
1. The volume of a cube can be calculated on length of his edge, having used formuloyv = a?, where an is cube edge length.
2. If as basic data there is only side diagonal length, then length of an edge can be found, having applied Pythagorean theorem, then the volume of a cube will be ravenv = (d/v2)?, where d is cube side diagonal.
3. Volume can be calculated, knowing diagonal most kubav = (d/v3)?, where d is cube diagonal.
4. If to enter the sphere in a cube, then its radius will be equal to a half of length of an edge of a cube, the volume of a cube will be ravenv = 8 * r?, where r is the radius of the sphere entered in a cube.
5. In case the sphere is described about a cube, then its radius will be equal to a half of diagonal of a cube, thus, the volume of a cube is calculated on formulev = (2R/v3)?, where R is the radius of the sphere described about a cube.