The surface area of a cube is an important part of elementary geometry. No matter if you have some problem to solve at school, prepare for an exam or just want to explore the world of three-dimensional objects, the calculation of surface area of a cube is fairly easy.
A cube has six equal square sides. The total area of the six sides is called its surface area. As soon as you know the length of one side, you can calculate the surface area of a cube in no time by applying a simple formula. In this guide we will show you how to do that, provide formulas for you, give examples and point out possible mistakes.
What Is the Surface Area of a Cube?
The surface area of a cube is the sum of the areas of all the outside faces of the cube.
A cube has: –
- 6 equal squares faces
- 12 equal sides
- 8 points 8 points 8 points
Since all faces of a cube are identical squares, you only need to know the length of one side to calculate its total surface area.
For example, imagine a cube with a side length of 4 centimeters. Each square face has an area of 4 × 4 = 16 square centimeters. Since there are six faces, the total surface area is 6 × 16 = 96 square centimeters.
Surface Area of a Cube Formula
The surface area of the cube formula is as follows:
SA = 6s²
Where:
SA = surface area of the cube
s = length of one side
s² = side length squared
6 = number of sides of a cube
This is because the cube has six sides that are all squares.
The area of one square side is:
Area = s × s = s²
Since a cube has six sides, therefore:
Surface Area = 6 × s²
Thus,
Surface Area of a Cube = 6s²
Note that surface area will always be in square units like cm², m², in², or ft².
How to Find Surface Area of a Cube
To get an idea of how to find the surface area of a cube, all that you have to do is follow these simple tips.
Step 1: Find the Length of the Side
See from the given data what the length of one side of the cube is.
Step 2: Squaring the Length of the Side
Get the value of the side length squared.
s² = s x s
Step 3: Multiply by 6
Use the formula to solve for the surface area of the cube:
SA = 6s²
Step 4: Squared Units
Express your answer in the correct squared units.
The above four tips should be able to help you solve most of the cube surface area problems.
More Examples of Surface Area of a Cube
More Examples of Surface Area of a Cube
Here are some additional examples to help you understand the calculation of the surface area of a cube.
| Side Length | Calculation | Surface Area |
|---|---|---|
| 2 cm | 6 × 2² | 24 cm² |
| 3 cm | 6 × 3² | 54 cm² |
| 4 cm | 6 × 4² | 96 cm² |
| 5 cm | 6 × 5² | 150 cm² |
| 10 cm | 6 × 10² | 600 cm² |
Practice Questions
Solve the following problems on your own:
- Determine the surface area of a cube whose side length is 3 cm.
- Calculate the surface area of a cube whose side length is 6 m.
- A cube has a side length of 8 inches. Calculate its surface area.
- A cube has a side length of 12 cm. What is its surface area?
- The surface area of a cube is 294 cm². Determine the side length.
Recommended Reading: How to Find the Surface Area of a Cuboid?
Conclusion
Calculating the surface area of a cube is easy, yet you will require one important formula.
SA = 6s²
You will have to calculate the length of the side, find its square, and then multiply the answer by 6 in order to solve any problem.
Therefore, when you learn about surface area of cube or the surface area of cube formula, it is important to understand why this formula exists in order to solve your geometrical problems easily.
You can opt for our Advanced Math or Vedic Math+Mental Math courses. Our Math Quiz for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.
