Strictly speaking, such concept as cube perimeter, in mathematics does not exist. However by analogy with the surface area of a cube, the equal total area of all sides, it is possible to enter also a concept of perimeter of a cube. ""The sum of lengths of all edges of a cube"" will be the most logical definition of this term. This size can be useful, for example, at production of a framework of a cube.
It is required to you
- - cube;
- - ruler.
Instruction
1. To find cube perimeter, determine length of one of his edges and increase this number by 12. In the form of a formula this rule can be written down as follows: P = 12 * a, where: Р – cube perimeter, and – length of its party. The similar formula can be necessary if it is necessary to collect a framework of a cube equal to existing.
2. Example: the teacher decided to make the visual aid "cubic metre" - a cube framework with a length of edge of 1 meter. Question: how many meters of a pipe are required for production of model of a cube? Decision: 1 (m) * 12 = 12 meters.
3. If it is necessary to calculate the size of a cube which framework can be made of the available material (a wire, fittings, a pipe, a corner, etc.), divide this length into 12. Or, in the form of a formula: and = P / 12
4. Example: there is a piece of a wire 1 m long of 20 cm. It is required: to determine the maximum size of a framework of a cube which can be bent from this wire. Decision: 1 m 20 cm = 120 cm (we translate value of length one system of measurement).120 cm / 12 = 10 cm (we find the maximum length of an edge of a cube).
5. If cube volume is known, then for finding of its perimeter increase by the 12th root cubic of its volume.P = 12 * √³V where: V – cube volume, √³ - designation of a cubic root.
6. Example: how many meters of a corner are required for production of a cubic aquarium of 27 liters? Decision: transfer liters to cubic meters: 27/1000=0.027m³.Найдите from 0.027 cubic root (it will be length of one edge): √³0.027=0.3 (m). Increase edge length by 12: 0.3 * 12 = 3.6 (meters).
7. If cube surface area is set, then to find its perimeter, use the following ratios: S = 6 * and², P = 12 * and, where: S – cube surface area, from where: Р = 12 * √ (S/6) = 2 * 6 * √S/√6 = 2 * √S * √6 * √6/√6 = 2 * √S * √6 = 2√6√S, that is:. R = 2√6√S
8. Example: on the seasonal dacha established the capacity for water having the cube form. On its production left the 25th square meter of sheet iron. That the tank for water became stronger it decided to scald a metal corner. Question: how many the corner is required? Decision: use above the removed formula: Р = 2√6√25 ≈ 24.5 (meters).