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102 LearnersLast updated on September 13, 2025
Area of Cube
Area is the space inside the boundaries of a three-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of the cube.
What is the Area of Cube?
A cube is a three-dimensional figure where all six faces are squares of equal size. The area of a cube refers to the total surface area covered by its six faces.
Area of the Cube Formula
To find the surface area of a cube, we use the formula: 6 × a², where 'a' is the length of the side of the cube. Now let’s see how the formula is derived.
Derivation of the formula: Each face of the cube is a square with an area of a². Since there are six faces, the total surface area is 6 × (area of one face). Therefore, the surface area of the cube = 6 × a².
How to Find the Area of Cube?
We can find the area of the cube using the formula for surface area. Here’s how: If the side length 'a' is given, the surface area of the cube can be calculated using the formula Surface Area = 6 × a².
For example, if the side length 'a' is 4 cm, what will be the area of the cube? Surface Area = 6 × a² = 6 × 4² = 6 × 16 = 96 The surface area of the cube is 96 cm².
Unit of Area of Cube
We measure the area of a cube in square units. The measurement depends on the system used: In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).
In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).
Special Cases or Variations for the Area of Cube
Since a cube is a three-dimensional shape with equal sides, its surface area is calculated using the side length. Consider the following special cases:
Case 1: Variation in Side Length If the side length is doubled, the surface area becomes 4 times greater because the surface area formula is quadratic with respect to 'a'.
Case 2: Surface Area and Volume Relation If you know the surface area, you can find the side length and thus calculate the volume of the cube.
Tips and Tricks for Area of Cube
To ensure accurate results while calculating the area of the cube, here are some tips and tricks:
- Remember that all six faces of the cube are equal squares.
- If you are given the surface area and need to find the side length, use the formula a = √(Area/6).
- Ensure all measurements are in the same units before calculating.
Common Mistakes and How to Avoid Them in Area of Cube
It is common for people to make mistakes while finding the area of a cube. Let’s take a look at some mistakes and how to avoid them.
Mistake 1
Using the Wrong Formula
Ensure you use the formula 6 × a² for the surface area, not the volume formula, which is a³.
Mistake 2
Measuring the Area Using the Wrong Units
For the area to be in square meters (m²), the side length should be in meters.
Convert units where necessary.
Mistake 3
Confusing Surface Area with Volume
Remember, surface area is about the area covered by the faces, while volume is the space inside the cube.
Mistake 4
Using Different Units for Each Side
Ensure all side lengths are measured in the same unit before calculating the area.
Area of Cube Examples
Problem 1
The side length of a cube-shaped room is given as 5 m. What will be the area?
We will find the area as 150 m².
Explanation
Here, the side length 'a' is 5 m.
The surface area of the cube = 6 × a² = 6 × 5² = 6 × 25 = 150 m².
Problem 2
What will be the area of the cube if the side length is 7 cm?
We will find the area as 294 cm².
Explanation
If the side length is given, we use the formula Surface Area = 6 × a².
Here, the side length 'a' is 7 cm.
Hence, the area will be 6 × 7² = 6 × 49 = 294 cm².
Problem 3
The surface area of a cube is 384 m². What is the side length?
We find the side length as 8 m.
Explanation
To find the side length, we use the formula Surface Area = 6 × a².
Here, the surface area is given as 384 m².
Solving for 'a', we have: 384 = 6 × a² a² = 384/6 a² = 64 a = √64 = 8 m.
FAQs on Area of Cube
1.Is it possible for the surface area of a cube to be negative?
2.How to find the surface area of a cube if the side length is given?
3.How to find the side length of a cube if its surface area is given?
4.How is the volume of the cube calculated?
5.What is meant by the surface area of a cube?
Glossaries of Terms Related to Area of Cube
- Surface Area: The total area covered by the surface of a three-dimensional shape.
- Cube: A three-dimensional shape with six equal square faces.
- Side Length: The length of a side of the cube.
- Metric System: A measurement system where area is measured in square meters (m²), square centimeters (cm²), etc.
- Volume: The amount of space occupied by a three-dimensional shape, calculated as a³ for a cube.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
