How to find the surface area of a cube?

The cube has a lot of interesting mathematical properties and is known to people from ancient times. Representatives of some ancient Greek schools believed that the elementary particles (atoms) that make up our world are cube-shaped, and mystics and esotericists even deified this figure. And today, representatives of parascience attribute the cube to amazing energy properties.

A cube is an ideal figure, one of the five Platonic solids. Platonic body is Correct polyhedral figure satisfying three conditions:

1. All its edges and faces are equal.

2. The angles between the faces are equal (for a cube the angles between faces are equal to 90 degrees).

3. All the vertices of the figure touch the surface of the sphere described around it.

The exact number of these figures was called Ancient Greek mathematician Teethet Athenian, and the disciple of Plato Euclid in the 13th book of Origins gave them a detailed mathematical description.

The ancient Greeks, inclined to describe the structure of our world with the help of quantitative quantities, gave the Platonic bodies a deep sacral meaning. They believed that each of the figures symbolizes the universe's beginnings: the tetrahedron is fire, the cube is earth, the octahedron is air, icosahedron is water, dodecahedron is ether. The sphere described around them symbolized perfection, the divine principle.

So, a cube, also called hexahedron (from Greek "hex" - 6), is a three-dimensional regular geometric figure. It is also called a regular quadrangular prism or a rectangular parallelepiped.

The cube has six faces, twelve edges and eight vertices. In this figure, you can enter other regular polyhedra: a tetrahedron (a tetrahedron with faces in the form of triangles), an octahedron (octahedron), and an icosahedron (twenty-sided).

A diagonal of a cube is a segment joining two vertically symmetric vertices. Knowing the length of the edge of the cube a, one can find the length of the diagonal v: v = a ^3.

In the cube, as mentioned above, we can enter a sphere, and the radius of the inscribed sphere (denoted by r) will be equal to half the length of the edge: r = (1/2) a.

If the sphere is described around the cube, then the radius of the described sphere (we denote it by R) will be: R = (3/2) a.

Quite common in school problems: how to calculate the area The surface of the cube? It's very simple, it's quite obvious to imagine a cube. The surface of the cube consists of six faces in the form of squares. Therefore, in order to find the surface area of the cube, you first need to find the area of one of the faces and multiply by their number: S _n = 6a ^2.

Similarly, as we found the surface area of the cube, calculate the area of its lateral faces: S _b = 4a ^2.

From this formula it is clear that the two opposite faces of the cube are the bases, and the other four are the lateral surfaces.

You can find the surface area of the cube in another way. Considering the fact that a cube is a rectangular parallelepiped, one can use the concept of three spatial dimensions. This means that the cube, being a three-dimensional figure, has 3 parameters: length (a), width (b) and height (c).

Using these parameters, we calculate the area of the total surface of the cube: S _n = 2 (ab + ac + bc).

To calculate the area of the cube's lateral surface, the perimeter of the base must be multiplied by the height: S _b = 2c (a + b).

The volume of a cube is a product of three components - height, length and width:
V = abc or three adjacent edges: V = a ^3.