Area measures the amount of space inside a 2D shape (in square units). Volume measures the space inside a 3D shape (in cubic units).
Key area formulae:
- Rectangle: $A = lw$
- Triangle: $A = \frac{1}{2}bh$
- Parallelogram: $A = bh$
- Trapezium: $A = \frac{1}{2}(a+b)h$
- Circle: $A = \pi r^2$
Key volume formulae:
- Cuboid: $V = lwh$
- Prism: $V = \text{cross-sectional area} \times \text{length}$
- Cylinder: $V = \pi r^2 h$
- Cone: $V = \frac{1}{3}\pi r^2 h$
- Sphere: $V = \frac{4}{3}\pi r^3$
- Pyramid: $V = \frac{1}{3} \times \text{base area} \times h$
Surface area: sum of the areas of all faces.
Example: Volume of a cylinder with $r = 3$ and $h = 10$: $$V = \pi \times 9 \times 10 = 90\pi \approx 282.7\text{ cm}^3$$
Common error: using diameter instead of radius in circle or cylinder formulae; forgetting the $\frac{1}{3}$ in cone and pyramid volumes.