Five Graded Worked Examples
The best way to solidify your grasp of spherical geometry is through progressive problem-solving.
Example 1: Small Integer Radius (r = 3 cm)
V = 4/3 × π × 3³ = 4/3 × π × 27 = 36π ≈ 113.10 cm³
Example 2: Decimal Radius (r = 2.5 m)
2.5³ = 15.625 → V = 4/3 × π × 15.625 = 20.833π ≈ 65.45 m³
Example 3: Given Diameter (d = 14 cm, using π = 22/7)
r = 7 cm → V = 4/3 × (22/7) × 7³ = 4/3 × 22 × 49 = 4312 / 3 ≈ 1437.33 cm³
Example 4: Hollow Shell Sphere
Outer radius R = 5 cm, inner cavity r = 4 cm. Volume of material = 4/3 π (5³ - 4³) = 4/3 π (125 - 64) = 4/3 π (61) ≈ 255.52 cm³
Example 5: Volume in Terms of Pi
Radius r = 9 units: V = 4/3 × π × 729 = 972π cubic units.
