107 LearnersLast updated on August 5th, 2025
Surface Area of Cube and Cuboid
A cube and a cuboid are 3-dimensional shapes with flat surfaces. The surface area of these shapes is the total area covered by their outer surfaces. In this article, we will learn about the surface area of a cube and a cuboid.
What is the Surface Area of a Cube and a Cuboid?
The surface area of a cube and a cuboid is the total area occupied by their boundaries or surfaces. It is measured in square units.
A cube is a 3D shape with six equal square faces, while a cuboid has six rectangular faces. Both shapes have a total surface area, which is the sum of the areas of all their faces.
Surface Area of a Cube and a Cuboid Formula
Both a cube and a cuboid have six faces, and their surface areas are calculated by summing the areas of all these faces. Below are the formulas for calculating their surface areas.
For a cube: Total Surface Area (TSA) = 6a² Here, a is the length of a side of the cube.
For a cuboid: Total Surface Area (TSA) = 2(lb + bh + hl) Where l is the length, b is the breadth, and h is the height of the cuboid.
Surface Area of a Cube
The surface area of a cube is the total area of all six identical square faces. The formula to calculate the surface area of a cube is:
Surface Area = 6a² square units
Here, a is the side length of the cube.
Surface Area of a Cuboid
The surface area of a cuboid is the sum of the areas of all its rectangular faces. The formula to calculate the surface area of a cuboid is:
Surface Area = 2(lb + bh + hl) square units
Where l is the length, b is the breadth, and h is the height of the cuboid.
Volume of a Cube and a Cuboid
The volume of a cube is the space it occupies, calculated as: Volume of a cube = a³ cubic units
The volume of a cuboid is the space it occupies, calculated as: Volume of a cuboid = l × b × h cubic units
Confusing Side Length with Edge Length
Students sometimes confuse the side length of a cube with the edge length of a cuboid. Remember, in a cube, all edges are equal, while a cuboid has different edge lengths.
Mistake 1
Using Incorrect Formula for Surface Area
Some students mistakenly use the formula for the surface area of a cube when calculating the surface area of a cuboid and vice versa. Ensure you use the correct formula for each shape.
Mistake 2
Mixing Up Length, Breadth, and Height
In a cuboid, students might mix up which dimension is the length, breadth, or height. Clearly identify each before calculation.
Mistake 3
Incorrect Units
Students often forget to use square units for area calculations. Remember, the surface area is always measured in square units.
Mistake 4
Forgetting to Multiply by 2 in Cuboid Formula
While calculating the surface area of a cuboid, students sometimes forget to multiply the sum of the areas of the faces by 2. Always double-check the formula.
Mistake 5
Solved Examples of Surface Area of Cube and Cuboid
Find the surface area of a cube with a side length of 4 cm.
Surface Area = 96 cm²
Problem 1
Given a = 4 cm. Use the formula: Surface Area = 6a² = 6 × 4² = 6 × 16 = 96 cm²
Find the total surface area of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm.
Explanation
TSA = 62 cm²
Problem 2
Use the formula: TSA = 2(lb + bh + hl) = 2(5 × 3 + 3 × 2 + 2 × 5) = 2(15 + 6 + 10) = 2 × 31 = 62 cm²
A cube has a side of 7 cm. Find the total surface area.
Explanation
Surface Area = 294 cm²
Problem 3
Use the formula: Surface Area = 6a² = 6 × 7² = 6 × 49 = 294 cm²
Find the surface area of a cuboid with dimensions 6 cm by 4 cm by 3 cm.
Explanation
TSA = 108 cm²
Problem 4
TSA = 2(lb + bh + hl) = 2(6 × 4 + 4 × 3 + 3 × 6) = 2(24 + 12 + 18) = 2 × 54 = 108 cm²
The surface area of a cube is 150 cm². Find the side length.
Explanation
Side length = 5 cm
It is the total area of all six square faces of the cube, calculated as 6a².
1.What is the surface area of a cuboid?
2.How is the volume of a cube different from a cuboid?
3.What units are used for surface area?
4.Can a cube be considered a cuboid?
Common Mistakes and How to Avoid Them in the Surface Area of Cube and Cuboid
Students often make mistakes while calculating the surface area of a cube and a cuboid, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
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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
