How to measure the cube

The cube or hexahedron is a geometric figure that is a regular polyhedron. Moreover, each of its faces is a square. In order to solve the problem on a cube, in solid geometry, we need to know the basic geometric parameters such as edge length, surface area, volume, radii of the inscribed and circumscribed spheres.

You will need

• textbook on geometry and mathematics.

Instruction

1. So, in order to find the surface area of a cube, calculate the area of one face and multiply it on the total number, that is, use the formula: SN=6*x*x=6*x^2 where x is the edge length of the cube.Example. Let the edge length of the cube is 4 cm, then total surface area is equal to SN=6*4*4=6*4^2=96 cm^2.
2. In order to calculate the volume of a cube, you need to find the area of the base and multiply it by the height, edge length). And since the cube has all faces and edges are equal, then we obtain the following formula: V=x*x*x=x^3.Example. Let the edge length of a cube is 8 cm, then the volume V=8*8*8=512 cm^3.In mathematics there is such a thing as curly. Out of it came the expression "to Erect a number in the cube (third power of that number).
3. The radius of the inscribed sphere is given by: r=(1/2)*x.Example. Let the volume of a cube is 125 cm^3, then the radius of the inscribed sphere is calculated in two stages. First, find the edge length for this 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 at exactly six points.
4. The radius of the sphere described by the following formula: R=((3^(1/2))/2)*x.Example. Let the radius of the inscribed sphere r equal to 2 cm, then in order to find the radius of the sphere is described, it is necessary, first, to find the length of its edges: x=r*2=2^2=4 cm, and the second, and the radius: R=((3^(1/2))/2)*4=2*3^(1/2) see the Cube will touch the sphere at eight points. These points are its vertices.
5. The length of the diagonal of a cube can be calculated by the formula: d=x*(3^(1/2)).Example. Let the edge length of the cube is 4 cm, then, using the above formula, we get: d=4*(3^(1/2)) see it is Worth Recalling that the diagonal of a cube is called a segment, which connects two symmetrically located peaks and passes through its center. By the way, in Cuba there are four.