How to find a cube edge?

A cube is one of the simplest three-dimensionalobjects, both in stereometry, and in nature. Before you find the edge of the cube, you need to recall what a cube is. It is a rectangular parallelepiped having equal edges. In addition, the cube is a hexagon, whose faces are equal squares. To find the edge of a cube, you need to know its some parameters - the volume of the cube, the area of ​​the face, the length of the diagonal of the cube or the face.

1. In most cases, the problems of fourtypes in which there is an edge of a cube. It is to determine the length of the edge along the diagonal of the cube, along the diagonal of its face, along the volume of the cube and the area of ​​the face. The simplest of them is to find an edge over the area of ​​the face. After all, the face of the cube is a square with a side that is equal to the edge of the cube. Therefore, the area of ​​this face is equal to the edge of the cube, squared. From here, in order to find an edge, it is necessary to extract a square root from the area of ​​the face. a = vS a is the edge of the cube (length), S is the area of ​​one face.
2. It is even easier to find the face of the cube on the basis of its volume,since the volume of the cube will be equal to the construction of the length of the edge in the third power. Consequently, if we extract the cubic root (third degree) from the volume, we obtain the length of the edge a = vV (the cubic root), here a is the edge of the cube (length), and V is its volume.
3. How to find the length of an edge of a cube if the lengthsdiagonals. We denote: a is the edge of the cube (length), b is the diagonal of the face of the cube (length), and c is the diagonal of the cube (length). The diagonal of the edge and the faces of the cube form an equilateral rectangular triangle. We apply the Pythagorean theorem, where: a ^ 2 + a ^ 2 = b ^ 2, here (a ^ - exponentiation) It turns out: a = v (b ^ 2/2). Extracting the square root from half the square of the diagonal of its face, we find the length of the edge of the cube.
4. We find the length of the edge along the diagonal of the cube, where a =edge of the cube, b - diagonal of the face, c - diagonal of the cube. They form a rectangular triangle. We start from the theorem of Pythagoras where: a ^ 2 + b ^ 2 = c ^ 2. We apply the above dependence between the values ​​of a and b, substitute them in the expression b ^ 2 = a ^ 2 + a ^ 2. Having obtained: a ^ 2 + a ^ 2 + a ^ 2 = c ^ 2, we find: 3 * a ^ 2 = c ^ 2, obtaining a finite expression; a = v (c ^ 2/3).

If the cube parameters are set to obsolete,national and other specific units, then it should be translated into suitable metric analogs - cubic meters, decimeters, centimeters or millimeters.