# Surface Area of a Cube Formula

## What is a Cube?

• A cube is a 3-D solid shape, which has a total of 6 sides.

• A cube is one of the simplest shapes in three-dimensional space.

• Sometimes, the shape cube is considered as “cubic”.

• We can also say that a cube is considered as a block, where all the length, breadth, and height are the same.

• Along with that, a cube has 8 vertices and 12 edges such that 3 edges meet at one vertex point.

### Surface Area of Cube Definition

The definition of the surface area of cube states that if the total surface area is equal to the sum of all the areas of the faces of the cube. Since the cube has six faces, therefore, the total surface area of the cube will be equal to the sum of all six faces of the cube.

Since the surface of the cube is in the shape of a square. Hence, the area of each face of the cube can be said to be equal to the square of the edge. Let the length of the edge of a cube is a.

Area of one face = a2

There are a total of 6 faces. Therefore,

Total Surface Area of cube Formula = a2 + a2 + a2 + a2 + a2 + a2

Total Surface Area of cube Formula = 6a2

A cube consists of a ‘n’ number of square units. Hence the surface area is the space covered by these square units on the surface of the cube. Basically, the surface area is the sum of all the areas of all the shapes that cover the surface of the shape. In the case of a cube, the number of faces is 6. So the surface area will be the sum of all the areas of six faces.

Now, let us derive the formula for surface area for a given cube, to solve problems based on it.

### Surface Area of a Cube Formula

As per the definition of the cube we have discussed above, we know, the cube consists of 6 square faces. Let us consider, a cube whose length of the edges is denoted by the letter ‘a’.

We know, by the formula of area of a square = side2 = a2

Therefore, the total surface area of cube formula = 6 × (area of each side)

= 6 × a2 = 6a2 Square Unit.

### Solved Examples

Question 1) What is the surface area of a cube of side equal to 5 cm?

Solution) Given,

Side of the cube equals a = 5 cm

Total Surface Area of Cube formula = 6a2

= 6 × 5 × 5

= 6 × 25 cm2

= 150 cm2

Question 2) What is the surface area of a cube of side equal to 17 cm?

Solution) Given,

Side of the cube equals a = 17 cm

Total Surface Area of Cube formula = 6a2

= 6 × 172 cm2

= 6 × 289 cm2

= 1734 cm2