# Cube

In geometry, a **cube**^{} is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. A cube is a solid shape with six square faces. Each square face has the same side length and thus all the faces have the same size. A cube has 12 edges and 8 vertices. Each vertex refers to a corner where three edges of a cube meet.

Centered by | Face | Vertex |
---|---|---|

Coxeter planes | B_{2} |
A_{2} |

Projective symmetry |
[4] | [6] |

Tilted views |

## Properties of a Cube Shape

- It is a three-dimensional, square-shaped figure
- It has 6 faces, 12 edges, and 8 vertices
- All faces are in the shape of a square
- All sides have the same length
- Each vertex meets three faces and three edges
- The edges run parallel to those parallel to it
- All angles of a cube are right angles

## Surface Area of a Cube

The total surface area of a cube is defined as the area of its outer surface.

Since the cube has six square faces and each of the square faces is of the same size, the total surface area of a cube = 6 ✕ area of one face.

Area of one square face = edge ✕ edge = a ✕ a = a**²**

Therefore, the total surface area of the cube = 6a**²**

The total surface area of the cube will be equal to the sum of all six faces of the cube.

Let’s say the length of each edge is “a”.

## Lateral Surface Area of a Cube

The lateral surface area of the cube is the sum of areas of its square faces, excluding the area of the top and the bottom face.

So the lateral surface area of a cube = sum of areas of 4 faces = 4a²

## Volume of a Cube

The volume is calculated by multiplying the object’s length, breadth, and height. In the case of a **cube shape**, the length, width, and height are all of the same length. Let us refer to it as “a”.

Hence the volume of the cube is a** ✕ **a ✕ a = a³

**Length of Diagonal of Cube**

If a is the length of the side, then,

- Length of Diagonal of Face of the Cube = √2 a
- Length of Diagonal of Cube = √3 a