Surface Area & Volume
6 minQuiz at the end
Volume Formulas
| Shape | Formula |
|---|---|
| Cuboid | l × w × h |
| Cube | s³ |
| Prism | Area of cross-section × length |
| Cylinder | πr²h |
| Cone | ⅓πr²h |
| Pyramid | ⅓ × base area × height |
| Sphere | 4/3 πr³ |
Surface Area Formulas
| Shape | Formula |
|---|---|
| Cuboid | 2(lw + lh + wh) |
| Cube | 6s² |
| Cylinder | 2πr² + 2πrh |
| Cone | πr² + πrl (where l = slant height) |
| Sphere | 4πr² |
Examples
Cuboid 5 × 4 × 3:
- Volume = 5 × 4 × 3 = 60cm³
- SA = 2(20 + 15 + 12) = 2(47) = 94cm²
Cube, side 4cm:
- SA = 6 × 4² = 6 × 16 = 96cm²
Cylinder r=3, h=10:
- Volume = π × 9 × 10 = 90π ≈ 282.6cm³
Sphere r=3:
- Volume = 4/3 × π × 27 = 36π ≈ 113.1cm³
Units
Always check your units:
- Volume is in cubic units (cm³, m³)
- Surface area is in square units (cm², m²)