# How to find edge cube?

Ivan Orlov

April 10, 2013

14878

A cube is one of the simplest three-dimensional objects, both in stereometry and in nature. Before you find the edge of a cube, you need to recall what a cube is. It is a rectangular parallelepiped with 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 some of its parameters - the volume of the cube, the area of the face, the length of the diagonal of the cube or face.

- In most cases, there are four types of problems in which the edge of a cube is located. It is to determine the length of the edge along the diagonal of the cube, along the diagonal of its face, by the volume of the cube and the area of the face. The simplest of them is to find an edge across the facet area. After all, the face of the cube is a square with a side that is equal to the edge of the cube. Consequently, the area of this face is equal to the edge of the cube, squared. Hence, in order to find an edge, it is necessary to extract the square root from the area of the face. a = vS and - the edge of the cube (length), S - the area of one face.
- It is even easier to find the face of the cube based on its volume, since the volume of the cube will be equal to the erection of the edge length to the 3rd degree. Therefore, if we extract the cube root (third degree) from the volume, we get the edge length a = vV (cube root), here a is the edge of the cube (length), V is its volume.
- How to find the length of the edge of a cube, if the lengths of the diagonals are known. Denote: a - the edge of the cube (length), b - the diagonal of the face of the cube (length), c - the diagonal of the cube (length). The diagonal edges and faces of the cube form an equilateral right triangle between them. 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 of half the square of the diagonal of its face, we find the edge length of the cube.
- Find the edge length along the diagonal of the cube, where a is the edge of the cube, b is the diagonal of the face, and c is the diagonal of the cube. They all form a right triangle. We proceed from the Pythagorean theorem where: a ^ 2 + b ^ 2 = c ^ 2. Apply the above relationship between the values of a and b, we substitute them into the expression b ^ 2 = a ^ 2 + a ^ 2. Having received: a ^ 2 + a ^ 2 + a ^ 2 = c ^ 2, we find: 3 * a ^ 2 = c ^ 2, getting the final expression; a = v (c ^ 2/3).

If cube parameters are set in obsolete, national and other specific units, then you should convert them to suitable metric analogs - cubic meters, decimeters, centimeters or millimeters.