Surface Area of a Cube
Related Pages
Surface Area Formula
Surface Area of Prisms
Surface Area of a Sphere
More Geometry Lessons
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.
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
- A Cube’s Faces: A cube has 6 faces.
- Shape of Each Face: Each face of a cube is a perfect square.
- 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.
- 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?
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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