How to find the surface area of ​​the cube?

Cube has a number of interesting mathematical properties and is known to people since ancient times.Representatives of some of the ancient Greek schools believed that the elementary particles (atoms) that make up our world, have the shape of a cube, and mysticism and esoteric even worshiped this figure.Today, representatives parascience credited cube amazing energy properties.

Cube - an ideal figure, one of the five Platonic solids.Platonic body - this is the correct multi-faceted figure, satisfying three conditions:

1. All its edges and faces are equal.

2. The angles between the faces are equal (at the corners between the faces of the cube are equal and 90 degrees).

3. All figures relate to the top of the surface of the sphere described around it.

exact amount of these figures called Greek mathematician Theaetetus of Athens, a student of Plato and Euclid in the 13th book of the beginning gave them a detailed mathematical description.

Greeks are prone to using quantitative variables to describe the structure of the world, gave the Platonic solids deep sacral meaning.They believed that each of the figures represents the beginning of the universe: the tetrahedron - fire, the cube - earth, octahedron - air, the icosahedron - water, dodecahedron - ether.Scope is described around them symbolized perfection, divine.

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So, cube, also called the hexahedron (from the Greek. "Hex" - 6) - is the correct three-dimensional geometric figures.It is also called regular quadrangular prism or box.

have six faces of the cube, the twelve edges and eight vertices.In this figure, you can enter other regular polyhedra: the tetrahedron (tetrahedron with faces as triangles), the octahedron (octahedron) and the icosahedron (icosahedron).

diagonals of a cube called the segment connecting the two symmetric about the center of the top.Knowing the length of the cube edge a, you can find the length of the diagonal v: v = a3.

The Cube, as stated above, you can enter the sphere, with the radius of the inscribed sphere (denoted by r) is equal to half the length of an edge: r = (1/2) a.

If the sphere circumscribed around the cube, the radius of the sphere (denoted R) is equal to: R = (3/2) a.

Quite common problems in school question: how to calculate the surface area of ​​the cube?Very easy, just visualize a cube.The surface of the cube has six faces in the form of squares.Consequently, in order to find the surface area of ​​the cube, it is first necessary to find the area of ​​one of the faces and to increase their number: Sn = 6a2.

Just as we found the surface area of ​​the cube, calculate the area of ​​its lateral faces: Sb = 4a2.

From this formula it is clear that the two opposite faces of a cube - a base, and the other four - side surface.

To find the surface area of ​​the cube can be another way.Given the fact that the cube - a cuboid, you can use the concept of the three spatial dimensions.This means that the cube being a three-dimensional figure has three parameters: the length (a) and width (b) and altitude (c).

Using these parameters, calculate the total surface area of ​​a cube: Sn = 2 (ab + ac + bc).

To calculate the lateral surface area of ​​a cube, the perimeter of the base to be multiplied by height: Sb = 2c (a + b).

volume of the cube - is the product of three components - the height, length and width:
V = abc or three adjacent edges: V = a3.