Surface Area of a Cube

The surface area of a cube is the sum of all its sides. A cube has six equal sides, including four sides, a top, and a bottom. The calculation of a cube surface area has several practical applications. 

In this blog, you will learn what a cube is, the surface area for cube, and how to find the surface area of a cube using a formula. 

What is a Cube?

Before diving into surface area, first, we will understand what a cube is. A cube is a three-dimensional object that has:

• Six square faces: All the faces are identical squares.
• Equal edge lengths: All edges of a cube are the same length.
• Right angles: Each angle in a cube is a right angle (90 degrees).

What is the Surface Area of a Cube?

The surface area of an object is the sum of all its sides. The surface area of cube can be defined as the sum of its bases and the area of its lateral surfaces. As the cube has six equal squares (i.e, four sides, a top, and a bottom), the surface area will be the sum of all six squares. 

Categories of Cube Surface Area 

A cube’s surface area can be categorized into two ways;

Lateral Surface Area

It is the surface area covered by the four sides of a cube. Its formula is given by 

Where ‘a’ is the area of one side.

Total Surface Area

 It is an area covered by all sides of the cube, that are, four sides and two bases. 

Surface Area Formula for Cube

The surface area of 3d shapes is the total area that covers its outer surface. Every 3d object has a specific formula of surface area, depending on its shape. The surface area formula for cube is given as;

In which, ‘a’ is the area of its sides. 

In the below diagram, a cube is expanded, and all its six sides are shown. Each side has an area a2.

The unit of measurement for surface area of a cube is a unit square such as mm², cm², or m².

How to Find Surface Area of a Cube– Steps

It is easy to find the surface area of any cube by following the right steps. Let’s follow simple steps on how to find surface area of a cube.

• Identify the length of any side of a cube. Let it be ‘a.
• Find the square of the side ‘a’, it will be a².
• To find the total surface area, multiply the area of the side (a²) by 6. 
• To find the lateral surface area, multiply the area of the side (a²) by 4. 
• Always write the surface area in square units. 

How to Calculate Surface Area of a Cube 

We can easily calculate the surface area of any object once we understand the surface area and its formula. Let’s look at the examples on how to calculate surface area of a cube. 

Example 1:

The length of the side of the cube is 5 cm. Calculate the total surface area. 

To find the surface area, we will use the following formula.

The length of a side is 5 cm, 

The area of the side will be a² or 5², which is equal to 25. 

Now put the value in the formula.

Example 2:

The length of the side of a cube is 8 ft.. What will be the total surface area?

The length of a side is 8ft, and the area of a side will be 8²ft.

Put the value in the formula. 

Example 3:

Calculate the lateral surface area of a cube with a side length of 3 m.

The formula to find the lateral surface area of a cube is 

Put the value in the formula

Example 4:

The base area of a cube is 36 square units. What will be the surface area of the cube?

As the base area is 36, we will consider it the area of one side.

Put the value in the formula.

Conclusion 

The surface area of a cube is a simple yet important concept in geometry. By understanding the formula of a cube's Surface Area = 6 × a², you can easily calculate the surface area of any cube, whether it's a toy, a building material, or even a box for packaging.