Sphere Surface Area Calculator & Proofs
Calculate the total exterior area covering a sphere using Archimedes' theorem A = 4πr². Discover how sphere surface area relates to four times the area of its great circle.
Sphere Surface Area Formula
A = 4 × π × r²
A= Total surface area in square units (cm², m², in²)r= Radius of the sphereπ= Mathematical constant Pi (≈ 3.14159)
Step-by-Step Solution
- Find radius: If diameter is given, divide by 2 (
r = d / 2). - Square radius: Multiply radius by itself (
r²). - Multiply by 4π: Multiply
r²by 4 and then by π.
Worked Demonstration
For a sphere with radius r = 6 cm:A = 4 × π × 6² = 4 × π × 36 = 144π ≈ 452.39 cm².