# How many faces, edges, and vertices does a cube have?

Last Updated : 18 Feb, 2024

Cube is a 3-Dimensional Figure in which all dimensions are equal. A cube has 6 Square faces as all the sides of a cube are equal. The boundary where the faces of the cube meet are called the cube edges. The point at which the cube edges meet is called the cube vertices. A cube has 12 Edges and 8 vertices. In this article, we will learn about cube edges faces vertices in detail with a brief introduction to cubes.

## What is a Cube?

A Cube is a 3-Dimensional Solid figure whose all faces are square shaped. We can also say that a cube can be visualized in the form of a square prism. This is because the faces of a cube are in the form of a square and are also platonic solid in nature. The faces of a cube are also known as planes.

### Properties of a Cube

The properties of a cube are mentioned below:

• All the faces are square-shaped, which implies that the length, breadth, and height are the same.
• The angles between any two faces or surfaces are equivalent to 90°.
• The opposite planes are parallel to each other.
• The opposite edges are parallel to each other.
• Each of the faces forms an intersection with four faces.
• Each of the vertices intersects with three faces and three edges.

### Cube Examples

Examples of Cube include, Rubik’s Cube, Ice Cube, Die used in Ludo, Cubical Box Etc. A picture of examples of a Cube is attached below:

## How many Faces, Edges, and Vertices does a Cube have?

There are 6 faces, 12 edges, and 8 vertices in a cube. Let’s look into them in detail:

### Faces in Cube

There are six faces in a cube. The faces in a cube are in the shape of a square. Faces are flat surfaces bounded by line segments on four sides called edges. We can realize there are six faces in a cube by seeing the number written 1 to 6 on the faces of the die of Ludo.

### Edges in cube

There are 12 Edges in a Cube. Edges are the boundary of a flat surface. Edges are the line segment where are two faces of a geometrical figure. Edges meet each other at a point called Vertices.

### Vertices in Cube

There are 8 vertices in a Cube. Vertices are the points where edges meet. In a cube, a minimum of three edges meet at a vertex. Vertices are the corners of the cube. Vertices are dimensionless.

## Formula of Cube

A cube is a 3D figure. Hence, it will occupy space which is called the volume of the cube. Each face has an area that combines to give up the surface area of the cube. Let’s learn the Formula of the Cube. Let us assume each side of the cube measures ‘a’ units. Hence formulas for this cube are given as:

• Volume of Cube = (Side)3 = a3 cubic units
• Total Surface Area of the Cube = 6 ⨯ (side)2 = 6a2 square units
• Lateral Surface Area of the Cube = 4 ⨯ (side)2 = 4a2 square units
• Diagonal of Cube = √3 ⨯ side = √3 a units

## Sample Problems on Cube Faces Edges and Vertices

Problem 1: Find the surface area of the cube if its side is 6 cm

Solution:

Given:

Side of the cube = 6 cm

As we know that

Surface area of the cube = 6 × side × side

⇒ Surface area of the cube = 6 × side2

⇒ Surface area of the cube = 6 × 62

⇒ Surface area of the cube = 216 cm2

Therefore,

Surface area of the cube is 216 cm2.

Problem 2: Find the volume of the cube if its side is 4 m2.

Solution:

Here we need to find the volume of the cube

Given:

Side of the cube = 4 m2

As we know that

Volume of the cube = Side × Side × Side

⇒ Volume of the cube = Side3

⇒ Volume of the cube = 43

⇒ Volume of the cube = 4 × 4 × 4

⇒ Volume of the cube = 64 m3

Therefore,

Volume of the cube is 64 m3.

Problem 3: Find how many small cubes can be made from a big cube of side 16 m in small cubes of side 4 m

Solution:

Here we need to find out how many small cubes can be made out of one big cube.

As we know that

Volume of cube = Side3

⇒ Volume of big cube = Side × Side × Side

⇒ Volume of big cube = 16 × 16 × 16

⇒ Volume of big cube = 163

⇒ Volume of big cube = 4096 m3

Further,

Volume of small cube = Side × Side × Side

⇒ Volume of small cube = 4 × 4 × 4

⇒ Volume of small cube = 43

⇒ Volume of small cube = 64 m3

Now,

Number of small cubes that can be made from the big cubes = Volume of big cube/Volume of small cube

⇒ Number of small cubes = 4096/64

⇒ Number of small cubes = 64

Therefore,

64 small cubes will be made out of the big cube.

Problem 4. If the surface area of a cube is 486 m2. Then find the volume of the cube.

Solution:

Here we need to find the volume of the cube from a given surface area

Given that Surface area of the cube = 486 m2

As we know that

Surface area of the cube = 6 × Side2

⇒ 486 = 6 × Side2

⇒ Side2 = 486/6

⇒ Side2 =  81

⇒ Side = √81

⇒ Side = 9 m

Now,

Volume of cube = Side3

⇒ Volume of cube = 93

⇒ Volume of cube = 9 × 9 × 9

⇒ Volume of cube = 729 m3

Therefore,

Volume of the cube is 729 m3.

## FAQs on Cube Faces Edges and Vertices

### Q1: Define Cube.

A Cube is a three-dimensional figure whose each face is a square.

### Q2: How many Faces are there in a Cube?

In a cube there are six faces.

### Q3: How many Edges are there in a Cube?

There are 12 Edges in a Cube.

### Q4: How many Vertices are there in a Cube?

A cube has 8 vertices.