# Surface Area of a Cube

In these lessons, we will learn
• how to calculate the surface area of a cube.
• how to find the length of a cube given the surface area.
• how to use the net of a cube to find its surface area.
• how to find the surface area of a cube in terms of its volume.
Related Topics: More Geometry Lessons

### Surface Area of a Cube

A cube is a three-dimensional figure with six equal square faces.
The surface area of a cube is the sum of the area of the six squares that cover it.

The figure above shows a cube. The dotted lines indicate edges hidden from your view.

If s is the length of one of its sides, then the area of one face of the cube is s2.

Since a cube has six faces the surface area of a cube is six times the area of one face.

Surface area of a cube = 6s2

Example

Find the surface area of a cube with a side of length 3 cm

Solution:

Given that s = 3

Surface area of a cube = 6s2 = 6(3)2 = 54 cm2

How to find the surface area of a cube? Example:
Given a side of 3 cm, find the surface area of the cube. How to find the surface area of a cube?
Step 1: Find the length of a side
Step 2: Substitute into the formula: side × side × 6 and evaluate
Step 3: Write the units How to find the length of a cube given the surface area?
This video shows how to find the length of a cube given the surface area.
Example: The total surface area of a cube is 216 in2. What is the length of each side of the cube?

How to use the net of a cube to find its surface area?

Another way to look at the surface area of a cube is to consider a net of the cube. The net is a 2-dimensional figure that can be folded to form a 3-dimensional object.

Imagine making cuts along some edges of a cube and opening it up to form a plane figure. The plane figure is called the net of the cube.

The following net can be folded along the dotted lines to form a cube.

We can then calculate the area of each square in the net and then multiply the area by 6 to get the surface area of the cube.

There are altogether 11 possible nets for a cube as shown in the following figures. Notice that the surface area of each of the net is the same.

How to use nets and 3-dimensional figures to find surface area of cubes and prisms? Surface Area of a Cube in terms of its Volume
How to find the surface area of a cube in terms of volume
S = 6V2/3

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