Ever wondered how much space the outside of a cube actually covers? That’s where surface area comes in! In simple terms, the surface area of a three-dimensional object is the total area of all its faces. When it comes to cubes—a favorite in geometry questions on the SAT, ACT, PSAT/NMSQT, GED, and even AP exams—you’re dealing with six square faces, all equal in size. So, knowing how to quickly calculate the surface area (along with volume and sometimes even perimeter) is super useful for test day.

We’ll walk you through exactly what surface area means for a cube, the formulas you need to memorize, and how to apply them step-by-step. Plus, we’ll throw in some solved examples to help you master this topic and confidently tackle any cube-related question that pops up on your next big test!

What is Surface Area of Cube?

Surface area of cube is the sum of the surface areas of six square faces of the given cube and a cube is made up of 6 square faces. Hence the surface area of a cube = 6 x surface area of a square.

Surface area of a square = length of one side x length of other side

Side length of a square = a

Hence surface area of a square = a²

Since a cube has six square faces,

The surface area of a cube = 6 x surface area of square = 6a².

There are 2 types of surface area of cube:

• Lateral surface area of cube
• Total surface area of cube

Lateral Surface Area of Cube

Lateral surface area of cube is the surface area covered by the four faces of a cube, except its top and bottom faces. The lateral surface area of a cube is equal to the sum of the areas of four faces of a cube.

Hence, lateral surface area of a cube formula is 4a², measured in unit square.

Total Surface Area of Cube

The total surface area of a cube refers to the sum of the total area covered by all six faces of the cube.

The total surface area of a cube formula is 6a², measured in unit square.

Total Surface Area of Cube Formula

Formula for Total Surface Area of Cube is 6a², where “a” is the length of each of its sides.

It is measured in square units.

Lateral Surface Area of Cube Formula

Formula for Lateral Surface Area of Cube is 4a², where “a” is the length of each of its sides.

It is measured in square units.

How to Find Surface Area of Cube

The total surface area of a cube is 6a² and the lateral surface area of a cube is 4a².

We can find surface area of a cube or lateral surface area of a cube by following below steps:

• Step 1: find the length of the side of the cube.
• Step 2: find the square of each of the lengths.
• Step 3: for total surface area of a cube, the square of each of the lengths will be multiplied by 6, i.e, 6a², for lateral surface area of a cube, the square of the lengths will be multiplied by 4, i.e, 4a².
• Step 4: write down your answer.

Solved Examples of Surface Area of Cube

Example 1: Find the total surface area of a cube, if its lateral surface area is 100 cm².

Solution 1: Given data,

Lateral surface area of a cube = 100 cm².

Lateral surface area of a cube formula = 4a².

Hence,

4a² = 100

100 / 4 = a²

a² = 25

a = 5cm² – which is the length of each side of a cube.

Total surface area of a cube formula = 6a² = 6 x 25 = 150cm².

The total surface area of the given cube is 150cm².

Example 2: Find the length of each side of a cube, if the total surface area of a cube is 100cm².

Solution 2: Given data,

The total surface area of a cube = 100cm².

Total surface area of a cube formula = 100cm².

6a² = 100

a² = 100 / 6

a² = 16.66

a = 4.081 cm.

The length of each side of a cube is 4.081 cm.

Example 3: The length of each side of a cube is 6ft, what will be its lateral surface area?

Solution 3: Given data,

The length of each side of a cube (a) = 6 ft.

Lateral surface area of a cube formula = 4a² = 4 x 36 = 144 ft².

The lateral surface area of a cube is equal to 144 ft².

Conclusion

And there you have it—understanding the surface area of a cube is easier than you think! Whether it’s the total surface area or lateral surface area, just remember those key formulas: 6a² and 4a². Mastering these will definitely give you an edge on exams like the SAT, ACT, PSAT/NMSQT, GED, and more. So, keep practicing, and soon, cube problems will feel like a breeze!