What is Surface Area and Volume?
- Surface Area is the total area of all the faces (surfaces) of a three-dimensional object. It is measured in square units (cm², m², etc.).
- Volume is the amount of space occupied by a three-dimensional object. It is measured in cubic units (cm³, m³, etc.).
Formulas for Basic 3D Shapes:
| Shape | Lateral/Curved Surface Area | Total Surface Area | Volume |
|---|---|---|---|
| **Cuboid** (l, b, h) | 2h(l + b) | 2(lb + bh + hl) | l × b × h |
| **Sphere** (radius = r) | — | 4πr² | (4/3)πr³ |
| **Hemisphere** (radius = r) | 2πr² | 3πr² | (2/3)πr³ |
| **Right Circular Cylinder** (r, h) | 2πrh | 2πr(r + h) | πr²h |
| **Right Circular Cone** (r, h, l) | πrl | πr(r + l) | (1/3)πr²h |
Key Terms:
- l = slant height = √(r² + h²) for a cone
- Lateral/Curved Surface Area = area of all faces except the base(s)
- Total Surface Area = lateral surface area + area of base(s)