Surface Area and Volume
5.4 Surface Area and Volume – Cheat Sheet
1. Surface Area Formulas
| Shape | Formula | Notes |
|---|---|---|
| Cuboid | SA = 2(lb + lh + bh) | l = length, b = breadth, h = height |
| Prism | SA = 2 × (area of cross-section) + (perimeter of cross-section × length) | Includes rectangular, triangular, etc. |
| Cylinder | SA = 2πr² + 2πrh | 2πr² = top + base, 2πrh = curved surface area |
| Sphere | SA = 4πr² | — |
| Pyramid | SA = base area + ½ × (perimeter of base × slant height) | Slant height (l) needed for lateral area |
| Cone | SA = πr² + πrl | πr² = base, πrl = curved surface |
2. Volume Formulas
| Shape | Formula | Notes |
|---|---|---|
| Cuboid | V = l × b × h | — |
| Prism | V = area of cross-section × length | — |
| Cylinder | V = πr²h | — |
| Sphere | V = ⁴⁄₃πr³ | — |
| Pyramid | V = ⅓ × base area × height | — |
| Cone | V = ⅓πr²h | — |
3. Key Notes
- All measurements in same units before substitution.
- Units:
- Surface area → unit² (cm², m²)
- Volume → unit³ (cm³, m³)
- Curved surface area (CSA) formulas to remember:
- Cylinder: CSA = 2πrh
- Cone: CSA = πrl
4. Quick Examples
- Volume of cone: r = 3 cm, h = 4 cm → V = ⅓π(3²)(4) = 12π cm³
- Surface area of sphere: r = 5 cm → SA = 4π(25) = 100π cm²