Pentagonal Pyramid Volume Calculator
Here’s a comprehensive table summarizing all you need to know about the volume of a pentagonal pyramid:
| Aspect | Details |
|---|---|
| Formula | V = (1/3) × A × h |
| Where | V = Volume A = Area of pentagonal base h = Height of pyramid |
| Base Area Formula | A = (5/4) × s² × tan(54°) |
| Where | s = Side length of pentagonal base |
| Alternate Formula | V = (5/6) × a × s × h |
| Where | a = Apothem length of pentagonal base s = Side length of pentagonal base h = Height of pyramid |
| Units | Cubic units (e.g., cm³, m³, in³) |
| Key Components | 1. Pentagonal base area 2. Pyramid height 3. Apothem length (if using alternate formula) |
| Calculation Steps | 1. Calculate base area (A) 2. Multiply by height (h) 3. Divide by 3 |
| Important Note | Ensure all measurements are in the same units |
| Variations | Regular pentagonal pyramid (all sides equal) Irregular pentagonal pyramid (sides may differ) |
| Relation to Other Formulas | Similar to other pyramid volume formulas, differing only in base area calculation |
This table provides a concise overview of the key information needed to calculate the volume of a pentagonal pyramid, including formulas, components, calculation steps, and important considerations.