Surface Area of a Sphere
The total surface area of a sphere.
Formula
Variables
Example
A sphere of radius 3: A = 4π·3² ≈ 113.1 square units.
How it works
The formula A = 4πr² gives the total area covering the outside of a sphere, like a ball or globe. It works because if you imagine the sphere sliced into many tiny pieces and flattened, those pieces collectively match the area of four circles with radius r. Since every point on a sphere is the same distance from the center, the radius alone determines its surface area.
When to use it
Use this formula when you need to find the amount of material needed to cover a spherical object, such as paint, wrapping, or metal coating. It is also used in geometry and physics whenever the outside area of a ball-shaped object matters.
Worked example, step by step
A sphere has radius 5 cm. A = 4πr² A = 4π(5)² A = 4π(25) A = 100π A ≈ 314.2 cm²
Common mistakes to avoid
- Using 2πr² instead of 4πr²
- Forgetting to square the radius before multiplying by 4π
- Mixing up surface area with volume, which uses r³ instead of r²
Did You Know?
A sphere's surface area equals exactly four times the area of its own shadow (a great circle).
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