Worked Solution: Volume of a Sphere with Radius 3
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 = 3 units.
⚡ Quick Numerical Summary:
- Radius (r): 3 units
- Diameter (d): 6 units
- Exact Volume (with π): 36π cubic units
- Decimal Volume: ≈ 113.10 cubic units
- Exterior Surface Area: ≈ 113.10 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 = 3) | r³ = (3)³ = 3 × 3 × 3 | 27 |
| Step 3 | Multiply by constant ⁴⁄₃ | ⁴⁄₃ × 27 = 36.00 | 36π (Exact) |
| Step 4 | Evaluate with π ≈ 3.14159265 | 36π × 3.14159265 | 113.10 |
Real-World Applications of r = 3
A sphere of radius 3 cm has a diameter of 6 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 0.113 Liters.