Cube - properties, patterns

The cube is a regular polyhedron with six sides, as the name suggests, in the shape of congruent squares. This is a special case of normal prism, hypercube, cuboid and rhombohedron. It can be found in nature as a sodium chloride or pyrite crystal. What does a cube look like? What is the formula for its surface area and volume? What are the properties?

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1. Properties of the cube

A cube (more precisely a regular hexahedron) is a regular polyhedron with six faces. Each wall has the shape of a congruent square. It has four edges, eight vertices, and twelve edges. If we cut the vertices of the cube properly, we get a semi-formic polyhedron, which we call a truncated cube.

The angle between the faces with a common edge is 90 °, and the solid angle at the vertex (triangular angle) is π / 2. The cube's symmetry group is Oₕ.

We can write a sphere into the cube or describe it on the cube.

Every cube is a cuboid, but not every cuboid is a cube.

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2. How to calculate the volume of a cube?

The formula for the volume of a cube is:

V = a³ = a × a × a

where a is the length of the cube edge.

3. Formula for the total area of ​​a cube

The formula is as follows:

S = 6a²

where a is the length of the cube edge.

The area of ​​the rectangle and its perimeter. Patterns and exercises

The area of ​​a rectangle can be calculated by multiplying the width of one side by the length of the other side. The condition is ...

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4. What is the formula for the length of the diagonal of the cube?

The formula looks like this:

d = a√3

where a is the length of the cube edge.

Diamond. Properties and patterns

A rhombus is a quadrilateral with sides of equal length. Everyone is a parallelogram and a deltoid - his ...

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## How to calculate the radius of a sphere inscribed in a cube and described on a cube?

Formula for the radius of a sphere inscribed in a cube:

r = a / 2

where a is the length of the cube edge.

Formula for the radius of a sphere described on a cube:

R = ½ d = ½ a√3

where a is the length of the cube's edge and d is its diagonal.

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