Comparing the Two Calculation Paths
Let us solve for the volume of a sphere of diameter 10 cm using both approaches side-by-side:
Radius MethodDiameter Method
Method A: Convert to Radius
1. r = 10 / 2 = 5 cm
2. V = 4/3 × π × 5³
3. V = 4/3 × π × 125 = 166.67π ≈ 523.60 cm³
Method B: Direct Diameter Formula
1. V = 1/6 × π × d³
2. V = 1/6 × π × 10³
3. V = 1/6 × π × 1000 = 166.67π ≈ 523.60 cm³