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290 LearnersLast updated on August 5, 2025
Surface Area of Cube and 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.
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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.
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
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