Surface Area of a Cube

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 total area of all its faces.

The following figure shows the formula for the surface area of a cube. Scroll down the page for more examples and solutions of finding the surface area of a cube.

Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Geometry Worksheets
Worksheet to calculate volume and surface area of cubes

Formula for the Surface Area of a Cube
The formula for the total surface area (SA) of a cube is: SA = 6s²

Where: SA = Total surface area of the cube s = the length of one side (or edge) of the cube

Explanation and Derivation of the Formula

1. A Cube’s Faces: A cube has 6 faces.
2. Shape of Each Face: Each face of a cube is a perfect square.
3. Area of One Face: The area of a single square face is calculated by multiplying its side length by itself, which is s × s = s².
4. Total Area: Since all 6 faces are identical squares, you multiply the area of one face by 6.
   Surface area of a cube (SA) = 6s².

How to Calculate the Surface Area of a Cube

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?

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Example:
Given a side of 3 cm, find the surface area of the cube.

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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

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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?

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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?

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Surface Area of a Cube in terms of its Volume
How to find the surface area of a cube in terms of volume
S = 6V^2/3

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