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Area and Volume Formulas: A Complete Quick Reference
From calculating room paint coverage to sizing shipping containers, area and volume formulas are essential everyday math. This reference covers all standard 2D and 3D shapes.
2D Area Formulas
| Shape | Formula | Variables |
|---|---|---|
| Square | aΒ² | a = side length |
| Rectangle | l Γ w | l = length, w = width |
| Triangle | Β½ Γ b Γ h | b = base, h = height |
| Circle | Ο Γ rΒ² | r = radius |
| Trapezoid | Β½ Γ (a + b) Γ h | a, b = parallel sides |
| Ellipse | Ο Γ a Γ b | a, b = semi-axes |
| Parallelogram | b Γ h | b = base, h = height |
| Regular polygon | Β½ Γ perimeter Γ apothem | apothem = center to mid-side |
3D Volume Formulas
| Shape | Formula | Variables |
|---|---|---|
| Cube | aΒ³ | a = edge length |
| Rectangular prism | l Γ w Γ h | l, w, h = dimensions |
| Sphere | (4/3) Γ Ο Γ rΒ³ | r = radius |
| Cylinder | Ο Γ rΒ² Γ h | r = radius, h = height |
| Cone | (1/3) Γ Ο Γ rΒ² Γ h | r = radius, h = height |
| Pyramid | (1/3) Γ base area Γ h | h = height |
| Hemisphere | (2/3) Γ Ο Γ rΒ³ | r = radius |
Surface Area Formulas
| Shape | Formula |
|---|---|
| Sphere | 4 Γ Ο Γ rΒ² |
| Cylinder | 2Οr(r + h) |
| Cone | Οr(r + slant height) |
| Cube | 6 Γ aΒ² |
Practical Applications
- Paint coverage: Measure wall area (L Γ H) minus window and door areas. One gallon covers approximately 350-400 square feet.
- Soil for garden beds: Length Γ Width Γ Depth in feet, divide by 27 to convert to cubic yards.
- Shipping costs: Volume in cubic inches / 139 = dimensional weight in pounds (UPS standard).
- Pool water volume: Use cylinder formula for round pools, rectangular prism for standard pools.