Sphere Formulas
Volume:
$V = \frac{4}{3}πr³$
Surface Area:
$SA = 4πr²$
Circumference:
$C = 2πr$ (great circle)
Where $r$ is the radius of the sphere.
Example:
For a sphere with radius 6 units:
- Volume = (4/3) × π × 6³ = (4/3) × π × 216 = 288π ≈ 904.78 cubic units
- Surface Area = 4π × 6² = 4π × 36 = 144π ≈ 452.39 square units
- Circumference = 2π × 6 = 12π ≈ 37.70 units
Properties:
- A sphere has the largest volume for a given surface area
- All points on the surface are equidistant from the center
- The diameter is twice the radius: d = 2r