Surface Area of a Sphere: Formula & Examples

The surface area of a sphere is A = 4 × π × r² (4πr²), where r is the radius of the sphere and π ≈ 22/7 or 3.14. Interestingly, the surface area of a sphere equals four times the area of its great circle (πr²). Quick example: a sphere with a radius of 7 cm has a surface area of 4 × (22/7) × 7² = 616 cm².

How to Calculate the Surface Area of a Sphere + Worked Example

A sphere is a solid whose entire surface is curved and equidistant (r) from a central point. Because it has no flat faces, its surface area needs just one formula:

Worked example: A football has a radius of 10.5 cm. What is the surface area of its outer skin? (π = 22/7)

Step 1: r = 10.5 cm. Step 2: r² = 110.25. Step 3: A = 4 × (22/7) × 110.25 = 4 × 346.5 = 1,386 cm².

So the surface area of the football is 1,386 cm².

Why It Matters

The surface area of a sphere is taught in Grade 9 (curved solids) and often appears in standardised tests. The concept is used in real life — estimating material to make balls, the surface area of planets, or the paint needed for a spherical tank. The formula 4πr² was first derived by Archimedes over 2,000 years ago.

See also: Surface Area of a Cylinder, Surface Area of a Cone, and Area of a Circle Formula. Browse everything at Algonova Mathematics.

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