Area of Cube
2026-02-28 11:05 Diff

137 Learners

Last updated on September 13, 2025

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.

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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.

Problem 1

The side length of a cube-shaped room is given as 5 m. What will be the area?

Okay, lets begin

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.

Well explained 👍

Problem 2

What will be the area of the cube if the side length is 7 cm?

Okay, lets begin

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.

Well explained 👍

Problem 3

The surface area of a cube is 384 m². What is the side length?

Okay, lets begin

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.

Well explained 👍

FAQs on Area of Cube

1.Is it possible for the surface area of a cube to be negative?

No, the surface area of a cube can never be negative. The area of any shape will always be positive.

2.How to find the surface area of a cube if the side length is given?

If the side length is given, then we find the area using the formula Surface Area = 6 × a².

3.How to find the side length of a cube if its surface area is given?

If the surface area is given, use the formula a = √(Surface Area/6) to find the side length.

4.How is the volume of the cube calculated?

The volume of a cube is calculated using the formula V = a³, where 'a' is the side length.

5.What is meant by the surface area of a cube?

The surface area of a cube is the total area covered by its six square faces.

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