how to find the surface area of a cube

Surface Area of Cube

The surface area of the cube can be defined as the total area covered by all six faces of the cube. The total surface area of a cube can be calculated if we calculate the area of the two bases and the area of the four vertical faces. A cube is a three-dimensional solid figure which consists of square faces. The surface area is important to know in the situations where we want to wrap a cube, paint the surfaces of the cube, etc.

1.	What is the Surface Area of Cube?
2.	Surface Area of Cube Formula
3.	Calculation of Surface Area of Cube
4.	FAQs on Surface Area of Cube

What is the Surface Area of Cube?

The surface area of the cube will be the sum of the area of the bases and the area of vertical surfaces of the cube. Since all the faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added five times to itself. It is measured as the "number of square units" (square centimeters, square inches, square feet, etc.). The surface area of a cube can be of two types,

Lateral surface area
Total surface area

Surface Area of Cube

Total Surface Area of Cube

The total surface area of a cube refers to the total area covered by all six faces of a cube. To calculate TSA, we find the sum of areas of these 6 faces.

Lateral Surface Area of Cube

The lateral surface area of a cube refers to the total area covered by the side or lateral faces of a cube. To calculate LSA, we find the sum of areas of these 4 faces.

Surface Area of Cube Formula

The surface area of a cube can be calculated given the edge length. Let us understand the formula for the lateral and total surface area of a cube.

Total Surface Area of Cube Formula

The formula of the total surface area of the cube is used to find the area occupied by the six surfaces. TSA of the cube is obtained by multiplying the square of its side length by 6. Thus, the formula for the surface area of the cube, with side length "a" is "6a²".

Total Surface Area of a Cube = (6 × side²) square units

Lateral Surface Area of Cube Formula

The formula of the lateral surface area of the cube is used to find the area occupied by the four lateral or side surfaces. LSA of the cube is obtained by multiplying the square of its side length by 4. Thus, the formula for the lateral surface area of the cube, with side length "a" is "4a²".

Lateral Surface Area of a Cube = (4 × side²) square units

Calculation of Surface Area of Cube

The total surface area of a cube is equal to the square of its side length times 6. Similarly, for lateral surface area, we multiply the square of side length by 4. By following the steps mentioned below we can find the surface area of the cube:

Step 1: Calculate the length of the side of the cube.
Step 2: Find the square of the length of the side of the cube.
Step 3: For total surface area, find out the product of the square of side length by 6, while for lateral surface area multiply the product of the square of side length by 4.
Step 4: Write your answer in square units.

Related Articles:

Check these interesting articles related to the concept of the surface area of cube.

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Surface Area Formulas
Surface Area of a Cube Calculator
Lateral Area of a Cube Formula
Surface Area of Cuboid

Surface Area of Cube Examples

Example 1: The length of the side of the cube is 15 in. Find the total surface area of the cube.

Solution:

Length of the side of the cube, a = 15 in.

Using the formula for the area of the cube, which is: A = 6a²,

A = 6 × 15 × 15

A = 1350

Therefore, the surface area of the cube is 1350 square inches.
Example 2: Olive has been given a cube of base area 64 square units. Find the length of the side of the cube and the total surface area of the cube.

Solution:

The base area of the cube = 64 square units.

Length of the side of the cube 'a' = √64 = 8 units.

Total surface area: A = 6a²

A = 6 × 8²

A = 384

So, the length of the base of the cube is 8 units, and the area of the cube is 384 square units.

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Practice Questions on Surface Area of Cube

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FAQs on Surface Area of Cube

What Is Meant By the Surface Area of a Cube?

The surface area of a cube is defined as the total area covered by the surfaces of a cube. To calculate the surface area of a cube, we find the sum of the area of all the faces of a cube.

What Is the Surface Area of Cube Formula?

The surface area of a cube with edge length as 'a' can be calculated using the following formulas, LSA of Cube = 4a² square units and, TSA of Cube = 6a² square units.

What Is the Unit Used to Express Surface Area of Cube?

The surface area of a cube is expressed in square units, for example using units like in², ft², yd², m², cm², etc.

What Is the Lateral Surface Area of a Cube?

The lateral area of a cube is the total area covered by the lateral or side surfaces of a cube. The formula to calculate the lateral surface area of a cube is given as, Lateral surface area = 4a², where, 'a' is the edge length of the cube.

What Is the Total Surface Area of Cube?

The total surface area of a cube is the area covered by all six faces of a cube. The formula to find the total surface area of a cube is given as, Total surface area = 6a², where, 'a' is the edge length of the cube.

What Is the Formula to Find the Area of the Base of a Cube?

The formula to find the area of the base of a cube is a², where a is the length of the side of the cube.