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Last updated on July 30th, 2025

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Surface Area of Cube and Cuboid

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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.

Surface Area of Cube and Cuboid for Australian Students
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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.

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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.

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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.

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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

Max Pointing Out Common Math Mistakes

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

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Using Incorrect Formula for Surface Area

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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

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Mixing Up Length, Breadth, and Height

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In a cuboid, students might mix up which dimension is the length, breadth, or height. Clearly identify each before calculation.

Mistake 3

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Incorrect Units

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Students often forget to use square units for area calculations. Remember, the surface area is always measured in square units.

Mistake 4

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Forgetting to Multiply by 2 in Cuboid Formula

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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

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Solved Examples of Surface Area of Cube and Cuboid

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Find the surface area of a cube with a side length of 4 cm.

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Hey!

Surface Area = 96 cm²

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Problem 1

Given a = 4 cm. Use the formula: Surface Area = 6a² = 6 × 4² = 6 × 16 = 96 cm²

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Okay, lets begin

Find the total surface area of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm.

Explanation

TSA = 62 cm²

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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

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Okay, lets begin

A cube has a side of 7 cm. Find the total surface area.

Explanation

Surface Area = 294 cm²

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Max, the Girl Character from BrightChamps

Problem 3

Use the formula: Surface Area = 6a² = 6 × 7² = 6 × 49 = 294 cm²

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Okay, lets begin

Find the surface area of a cuboid with dimensions 6 cm by 4 cm by 3 cm.

Explanation

TSA = 108 cm²

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Problem 4

TSA = 2(lb + bh + hl) = 2(6 × 4 + 4 × 3 + 3 × 6) = 2(24 + 12 + 18) = 2 × 54 = 108 cm²

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Okay, lets begin

The surface area of a cube is 150 cm². Find the side length.

Explanation

Side length = 5 cm

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Well explained 👍
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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?

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2.How is the volume of a cube different from a cuboid?

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3.What units are used for surface area?

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4.Can a cube be considered a cuboid?

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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.

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Fun Fact

: She has songs for each table which helps her to remember the tables

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