Cube – one of the simplest volume figures. It consists of six sides which are crossed at right angle being equal squares. Lines of crossing of sides of a cube are called his edges, and points of intersection of edges – tops. Sometimes it is possible to hear also such "term" as "party" of a cube. Depending on a specific situation both the cube side, and his edge can be meant by this concept. In life and games (when using a cube as a dice) the party of a cube usually call its side. If the pupil tries to find the party of a cube, then for certain it is required to determine length of his edge (a cube, but not the pupil).
It is required to you
- calculator
Instruction
1. A cube so symmetric figure that for finding of its party (edge) it is enough to know at least one of key parameters of a cube. Its volume, the area of a side, length of diagonal of a side and length of diagonal of a cube (so-called "big diagonal") belong to them. To find the party of a cube if the area of its side is known, take a square root from numerical value of the area of a side. In the form of a formula this dependence can be written down in the following look: With = p, where: With – length of the party (side) of a cube, P - the area of a side of a cube. This formula is brought out of the fact that the side of a cube represents a square with the party equal to a cube edge, and the area equal to an edge square.
2. Finding of the party (edge) of a cube on the set volume is similar. As the volume of a cube is equal to the third degree (cube) of length of his edge, for determination of length of an edge of a cube take a cubic root from its volume. That is use a formula: With =³ √ About, where About – cube volume. ³ √ - function of extraction of a cubic root).
3. For finding of the party (edge) of a cube on the diagonal of its side take a square root from the square of diagonal halved. In the form of a formula this rule looks as follows: With = √ (d²/2), where d – cube side diagonal length. Justice of this formula follows from Pythagorean theorem as the diagonal and two adjoining edges form an equilateral rectangular triangle where diagonal is a hypotenuse, and edges – legs.
4. To find the party (edge) of a cube on its diagonal (cube diagonals, but do not facet), take a square root from a third of a square of length of this diagonal. That is, use a similar previous formula: With = √ (Д^2/3). This formula is also removed on the basis of Pythagorean theorem as cube diagonal, the diagonal of a side and an edge of a cube form rectangular (but, unequalateral) a triangle.