Surface Area of Cubes – SA = 6s²
A cube's surface area is simply the total area of its 6 identical square faces. Since each face has area s² (side times side), and there are 6 of them, the full formula is SA = 6s². This is one of the simplest surface area formulas in geometry, precisely because every face on a cube is exactly the same.
You met this same 6s² formula briefly on the main Surface Area overview page – here, we'll go deeper, including working backwards from a known surface area to find the cube's side length.
Calculating a Cube's Surface Area
SA = 6s², where s is the length of one side. To reverse the formula and find s from SA, divide by 6 and take the square root.
Find the surface area of a cube with side 5 cm.
SA = 6 × 5² = 6 × 25 = 150 cm².
A cube has a surface area of 96 cm². Find its side length.
s² = 96 ÷ 6 = 16, so s = √16 = 4 cm.
Real-Life Application
- Packaging: the cardboard needed for a cube-shaped box equals its surface area.
- Painting: the paint needed to cover a cube-shaped object depends on its surface area.
- Wrapping gifts: estimating wrapping paper for a cube-shaped present.
Key Takeaways
- A cube's surface area formula is SA = 6s².
- To find the side from a known surface area, divide by 6 and take the square root.
- All 6 faces of a cube contribute equally to its total surface area.
Practice: Surface Area of Cubes
Surface Area of Cubes
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