# How to measure the cube

The cube or hexahedron - a geometric figure, which is a regular polyhedron. Moreover, each of its faces is a square. In order to solve the problem in the cube in solid geometry, it is necessary to know the basic geometric parameters such as the length of an edge, surface area, volume, the radii of the inscribed and circumscribed sphere.

### You will need:

textbook on geometry and mathematics.

## Instruction how to measure cubic

Step 1:

So, in order to find the surface area of the cube, calculate the area of one face and multiply it by the total amount, that is, use the formula: Sn = 6 * x * x = 6 * x ^ 2, where x - is the length of the rib kuba.Primer . Let cube edge length of 4 cm, then the total surface area is equal to Sn = 6 * 4 * 4 = 6 * 4 ^ 2 = 96 cm ^ 2.

Step 2:

In order to calculate the volume of a cube, you need to find a footprint and multiply it by the height (edge length). And since all of the cube faces and edges are equal, then the following formula: V = x * x * x = x ^ 3. Example. Let the length of the edge of the cube is 8 cm, while the volume of V = 8 * 8 * 8 = 512 cm ^ 3. In mathematics there is such a thing as a figure number. It is because of him and went the expression: "Raise number into a cube" (Third degree to find this number).

Step 3:

The radius of the sphere is inscribed by the formula: r = (1/2) * x.Primer. Let the volume of the cube is equal to 125 cm ^ 3, then the radius of the inscribed sphere is calculated in two steps. First, find the edge length, for that calculate the cube root of 125. It will be 5 cm. And then calculate the radius of the inscribed sphere r = (1/2) * 5 = 2.5 cm. By the way, the sphere will touch the cube exactly six points.

Step 4:

The radius of the sphere is calculated as follows: R = ((3 ^ (1/2)) / 2) * x.Primer. Let the radius of the inscribed sphere r is 2 cm, while in order to find the radius of the sphere, it is necessary, first, to find the length of its edge: x = r * 2 = 2 ^ 2 = 4 cm, and secondly, already. itself radius: R = ((3 ^ (1/2)) / 2) = 4 * 3 * 2 ^ (1/2) cm cube sphere is in contact with eight points.. These points are vertices.

Step 5:

The length of the diagonal of the cube can be calculated according to the formula: d = x * (3 * (1/2).) Example. Let cube edge length is 4 cm, then using the above formula, we obtain: d = 4 * (3 ^ (1/2)) sm.Stoit recalled that inch cube called a segment that connects two symmetrically disposed top and passes through its Centre. By the way, there are four cubes.