How to Find the Radius of a Sphere: Inverse Formulas & Examples

Solving for Radius from Different Known Dimensions

Depending on what data you have, use the appropriate inverse algebraic rearrangement:

1. From Diameter: r = d / 2
2. From Circumference: r = C / (2π)
3. From Surface Area: r = √( A / (4π) )
4. From Volume: r = ∛( (3V) / (4π) )

Worked Problem: Solving Radius from Volume V = 1000 cm³

Follow these steps to solve for radius when = 1000 ext{ cm}^3$:

• Multiply volume by 3: $3 imes 1000 = 3000$.
• Divide by $4\pi$: $3000 \div (4 imes 3.14159265) \approx 3000 \div 12.56637 \approx 238.73$.
• Take cube root: $\sqrt[3]{238.73} \approx 6.20 ext{ cm}$.