If on the plane the square can be compared on primitiveness degree only to an equilateral triangle, then four more regular polyhedrons compete to a cube. Nevertheless, it is very simple, maybe, even more simply than a tetrahedron.
Instruction
1. What is a cube? Otherwise this form call a hexahedron. It is the simplest of prisms, its parties at a cube are in pairs parallel as they at any of prisms, and are equal. You can also find out that the hexahedron is called a parallelepiped. Indeed. The cube is a rectangular parallelepiped with equal edges, each of six sides of which is a square. In each top of a cube three of his edges, thus all at it – six sides, eight tops and twelve edges meet, the adjoining sides are perpendicular each other, that is create corners in 90 °.
2. If you at the beginning of calculations have no data on a cube, arrive simply. Call an edge of a cube and. Now you will also make a start from this most non-numerical value when calculating.
3. If one of edges of a cube and, then any other edge of a cube equals and. Area of a side of a cube always а^2. Diagonal of a side of a cube is calculated on Pythagorean theorem and equals and to increase by a root from two. All aforesaid results from the fact that each side of a cube – a square, so the edge of a cube is in each case the party of a square, and the side of a cube equals the areas of a square with the party and.
4. Now will pass to formulas of the following order. Knowing the area of one side of a cube, it is easy to find out the area of its surface, it is equal 6а^2. The volume of a cube equals а^3 as the area of any direct prism is equal to the work of length of a prism on width and on its height, and all these parameters are equal in our case and.
5. Length of diagonal of a cube is equal and to increase by a root from 3. It is clear from the theorem that the square of diagonal is equal in any rectangular parallelepiped to the sum of squares of three linear dimensions of this polyhedron. In the place of crossing of diagonals of a cube, or other parallelepiped, there is a symmetry point. The point divides diagonals equally, besides, cubed through a point of symmetry there pass nine planes of symmetry dividing a cube into equal parts. Here you also learned all data necessary and sufficient to calculate any parameter of a cube. Try.