Worked Solution: Volume of a Sphere with Radius 4
Welcome to the complete, step-by-step mathematical walkthrough for finding the volume, surface area, and fluid capacity of a sphere having a radius of exactly r = 4 units.
⚡ Quick Numerical Summary:
- Radius (r): 4 units
- Diameter (d): 8 units
- Exact Volume (with π): 85.33π cubic units
- Decimal Volume: ≈ 268.08 cubic units
- Exterior Surface Area: ≈ 201.06 square units
Step-by-Step Mathematical Solution
| Step | Action | Formula & Algebraic Working | Result |
|---|---|---|---|
| Step 1 | State the standard formula | V = ⁴⁄₃ × π × r³ | Formula stated |
| Step 2 | Substitute radius (r = 4) | r³ = (4)³ = 4 × 4 × 4 | 64 |
| Step 3 | Multiply by constant ⁴⁄₃ | ⁴⁄₃ × 64 = 85.33 | 85.33π (Exact) |
| Step 4 | Evaluate with π ≈ 3.14159265 | 85.33π × 3.14159265 | 268.08 |
Real-World Applications of r = 4
A sphere of radius 4 cm has a diameter of 8 cm. In everyday physics and industry, spheres of this size approximate common sports equipment, ball bearings, optical lenses, or storage vessels. Its capacity in liquid measure equals 0.268 Liters.