Mathematical Formula
V = ⁴⁄₃ × π × r³
Where V = Volume, r = Radius, and π ≈ 3.14159265
Alternative Formula with Diameter (d): V = ¹⁄₆ × π × d³ (since r = d/2 and (d/2)³ = d³/8).
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| Geometric Quantity | Formula (Using Radius r) | Formula (Using Diameter d) |
|---|---|---|
| Volume | V = ⁴⁄₃πr³ | V = ¹⁄₆πd³ |
| Surface Area | A = 4πr² | A = πd² |
| Circumference | C = 2πr | C = πd |
| Radius from Volume | r = ∛(3V / 4π) | d = ∛(6V / π) |
| Radius from Surface Area | r = √(A / 4π) | d = √(A / π) |
| Hemisphere Volume | V = ⅔πr³ | V = ¹⁄₁₂πd³ |
| Hemisphere Total Area | A = 3πr² | A = ¾πd² |