Surface Area of a Cube
Total surface area of a cube.
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Example
A cube of side 4: A = 6·4² = 96 square units.
How it works
A cube has 6 identical square faces, and each face has area a² because its side length is a. The total surface area is therefore 6 times the area of one face, giving A = 6a². This formula counts every outer face of the cube, so it tells you how much material would be needed to cover the outside.
When to use it
Use this formula when you need the outside area of a cube, such as wrapping a box, painting a cube-shaped object, or finding the amount of paper, metal, or cardboard needed. It is also useful in geometry problems that ask for total surface area from a given edge length.
Worked example, step by step
Find the surface area of a cube with edge length 7 cm. A = 6a² A = 6 × 7² A = 6 × 49 A = 294 Final answer: 294 cm²
Common mistakes to avoid
- Using 4a² instead of 6a² and forgetting that a cube has 6 faces
- Finding the area of just one face instead of the total outside area
- Mixing up edge length with volume and using a³ instead of a²
Did You Know?
A cube has 6 identical square faces, so its surface area is simply six times one face.
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