Worked Solution: Volume of a Sphere with Radius 1
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 = 1 units.
⚡ Quick Numerical Summary:
- Radius (r): 1 units
- Diameter (d): 2 units
- Exact Volume (with π): 1.33π cubic units
- Decimal Volume: ≈ 4.19 cubic units
- Exterior Surface Area: ≈ 12.57 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 = 1) | r³ = (1)³ = 1 × 1 × 1 | 1 |
| Step 3 | Multiply by constant ⁴⁄₃ | ⁴⁄₃ × 1 = 1.33 | 1.33π (Exact) |
| Step 4 | Evaluate with π ≈ 3.14159265 | 1.33π × 3.14159265 | 4.19 |
Real-World Applications of r = 1
A sphere of radius 1 cm has a diameter of 2 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 0.004 Liters.