How to Find the Surface Area of a Cube
How to Find the Surface Area of a Cube in 3 Easy Steps
Learning how to find the surface area of a cube and how to apply the surface area of a cube formula is a critical and important math/geometry skill that every student should master. Fortunately, calculating the area of a cube is a pretty straightforward task as long as you are able to follow three simple steps for finding the surface area of any cube that are demonstrated in this lesson.
Are you ready to get started?
The following free How to Find the Surface Area of a Cube lesson guide is a step-by-step tutorial that will teach you how to use a simple method for calculating the surface area of a cube using the surface area of a cube formula to solve homework problems, test questions, and more.
This guide also includes a completely free surface area of a cube calculator that can be used to make fast calculations and find the surface area of a cube almost immediately (and while we do not recommend relying on a calculator to solve surface area problems, having access to a calculator can be a very helpful tool when it comes to checking your work—but more on that later!)
Now we are ready to learn how to find the surface area (sometimes referred to as SA) of a cube and we will start with a quick recap of some very important vocabulary and definitions.
In math, what is a cube?
Definition: A cube is a box-shaped three-dimensional figure that has six equal and identical square faces.
The most important word in this definition is equal. A cube is unique in that all of its faces are squares with side lengths, also known as edges, that have the same length (unlike rectangular prisms).
Also make a note that the terms cube and rectangular cube both mean the exact same thing (some questions will refer to a cube as a rectangular cube).
What is the surface area of a cube? What is the SA of a cube?
Definition: The surface area of a cube refers to the total area of all of the faces on the outside of the figure.
The key word in this definition is outside since surface area refers to how many square units it would take to cover the outside of the figure
Surface area is always expressed in square units.
Surface Area of a Cube Formula
Before we get to the practice problems, you need to understand how to use the surface area of a cube formula, which states that the SA of a cube is equal to six times the side length, s, raised to the second power (also known as squared).
If you know the length of one of the edge lengths (or sides), you can simply input the value into the formula and solve to find the surface area.
Again, remember that SA is measured in square units and that your answers should always include units.
Formula Reference:
Now that you know the surface area of a cube formula, you can use the following 3-step method to solve the practice problems below:
Step 1: Identify the value of s, the edge length of the cube
Step 2: Substitute that value for s into the surface area of a cube formula
Step 3: Solve and express your answer in square units
Example #1: Find the Surface Area of the Cube
Find the surface area of a cube with a side length of 4 cm.
To solve this problem, we will use the previously mentioned 3-step process:
Step 1: Identify the value of s, the edge length of the cube
In this example, the cube has a side length of 4 cm, so S=4
Step 2: Substitute that value for s into the surface area of a cube formula
Next, substitute 4 for s in the SA of a cube formula as follows
SA = 6(s^2) ➝ SA= 6(4^2) ➝ SA = 6(16) ➝ SA = 96
Step 3: Solve and express your answer in square units
Finally, you can conclude that SA equals 96, therefore…
Final Answer: The surface area of the cube is 96 square centimeters.
Remember that surface area is always expressed in square units (square centimeters in this example).
Example #2: Find the SA of the Cube
Find the SA of a cube-shaped box with a height of 9 inches.
In this example, the figure in question is a cube-shaped box or just a cube, so you will be using the process as Example #1 to find the surface area:
Step 1: Identify the value of s, the edge length of the cube
In this example, the cube-shaped box has a side length of 9 inches, so S=9
Step 2: Substitute that value for s into the SA of a cube formula
Next, substitute 9 for s in the SA of a cube formula as follows
SA = 6(s^2) ➝ SA= 6(9^2) ➝ SA = 6(81) ➝ SA = 486
Step 3: Solve and express your answer in square units
Finally, you can conclude that SA equals 486, therefore…
Final Answer: The SA of the cube is 486 square inches
How to Find the Surface Area of a Cube Video
Are you looking for more help with finding the volume and surface area of cubes? Check out our free step-by-step video lesson below:
Surface Area of a Cube Calculator
If you want to use a surface area of a cube calculator to help you when solving SA problems, we recommend Google’s free Surface Area of a Cube Calculator, which allows you to input the edge length (which they refer to as a instead of s) and find the SA with just one click.
Keep in mind that relying on a calculator is never a substitute for learning how to solve problems on your own. However, there are occasions when such a tool can come in handy, like when you want to check your final answers.
(Note: Google’s calculator uses the letter a, not s, to represent the value of the edge length.)
What About the VOLUME of a Cube?
Now that you’ve learned how to find the surface area of a cube, you’re ready to move on to learning how to use a different formula to find the volume of a cube.
You can use the link below to access our free guide to finding the surface area of a cube.
Click here to access a free Volume of a Cube step-by-step guide.
Conclusion: How to Find the Surface Area of a Cube
You can find the SA of any cube with edge length S by following this easy 3-step process:
Step 1: Identify the value of s, the edge length of the cube
Step 2: Substitute that value for s into the surface area of a cube formula
Step 3: Solve and express your answer in square units