Volume of a Sphere
The space inside a sphere of radius r.
V = \dfrac{4}{3}\pi r^3
1What it means
The volume of a sphere depends on the cube of the radius, so a small change in radius changes the volume a lot.
2Variables
| Symbol | Meaning |
|---|---|
| V | Volume |
| r | Radius |
| \pi | Pi ≈ 22/7 |
3Worked examples
Example 1 Worked solution
Q. Find the volume of a sphere of radius 3 cm (π ≈ 3.14).
- V = (4/3) π r³ = (4/3) × 3.14 × 3³.
- = (4/3) × 3.14 × 27.
- = 4 × 3.14 × 9.
✓ V ≈ 113.04 cm³
4Where it's used
- ✦Volume of balls, bubbles, planets and droplets.
5Tips & common mistakes
- !It is r³, not r² — cube the radius.
- !Surface area of a sphere is 4πr² (a different formula).