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Surface Area of a Sphere

SA = 4πr²

📖 What is the Surface Area of a Sphere?

The surface area of a sphere is the total area of its outer curved surface. Notice that 4πr² is exactly four times the area of a circle with the same radius. Archimedes first proved this remarkable relationship.

SA = 4 × π × r²

🔤 Variables

SA
Surface Area (square units)The total area of the sphere's outer surface
r
RadiusThe distance from the centre to the surface
π
Pi ≈ 3.14159Mathematical constant

📝 Example

A basketball has radius 12 cm. What is its surface area?

1
Identify radiusr = 12 cm
2
Apply formulaSA = 4 × π × 12² = 4 × π × 144
✓
Answer: SA ≈ 1809.56 cm²

🧮 Interactive Calculator

Result will appear here

💡 Volume vs Surface Area

Volume of Sphere:
V = (4/3)πr³
Surface Area of Sphere:
SA = 4πr²
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🔗 Related

🎯 Quick Fact

Archimedes was so proud of discovering that a sphere's surface area = 4 × circle area that he asked for a sphere-in-cylinder diagram to be carved on his tombstone.