Hexagonal Pyramid Volume Calculator

Base Edge Length \( a \):

Height \( h \):

Apothem \( a_p \)

Apothem (cm): Apothem (m): Apothem (in): Apothem (ft):

Slant Height \( l \)

Slant Height (cm): Slant Height (m): Slant Height (in): Slant Height (ft):

Base Perimeter \( P \)

Base Perimeter (cm): Base Perimeter (m): Base Perimeter (in): Base Perimeter (ft):

Volume \( V \)

Volume (cm³): Volume (m³): Volume (in³): Volume (ft³): Volume (liters):

1. What is a Hexagonal Pyramid Volume Calculator?

Definition: This calculator computes the volume, base edge length, apothem, slant height, and base perimeter of a regular hexagonal pyramid based on the length of the base edge (\( a \)) and the height (\( h \)). A regular hexagonal pyramid has a base that is a regular hexagon.

Purpose: Useful in geometry, architecture, and engineering for analyzing hexagonal pyramid structures.

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ V = \left(\frac{\sqrt{3}}{2}\right) \times a^2 \times h \] \[ a_p = \left(\frac{\sqrt{3}}{2}\right) \times a \] \[ P = 6 \times a \] \[ l = \sqrt{h^2 + a_p^2} \]

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Volume (from cm³): m³ (×0.000001), in³ (×0.0610237), ft³ (×0.0000353147), liters (×0.001)
Length (from cm): m (×0.01), in (×0.393701), ft (×0.0328084)

Explanation: All dimensions are converted to cm, the base perimeter, apothem, volume, and slant height are calculated, and then converted to other units.

3. Importance of Hexagonal Pyramid Volume Calculation

Details: Calculating the volume, base edge, apothem, slant height, and base perimeter of a hexagonal pyramid is essential in architecture (e.g., designing pyramid roofs), engineering, and geometry education.

4. Using the Calculator

Tips: Enter the base edge length \( a \) and height \( h \) in mm, cm, m, in, or ft (both must be >0). The result shows the base edge length, apothem, slant height, and base perimeter in cm, m, in, and ft, and the volume in cm³, m³, in³, ft³, and liters.

5. Example

Given: Base edge length \( a = 4 \, \text{cm} \), height \( h = 10 \, \text{cm} \).
Base Perimeter Calculation: \( P = 6 \times 4 = 24 \, \text{cm} \).
Apothem Calculation: \( a_p = \left(\frac{\sqrt{3}}{2}\right) \times 4 \approx 3.464 \, \text{cm} \).
Volume Calculation: \( V = \left(\frac{\sqrt{3}}{2}\right) \times 4^2 \times 10 \approx 138.564 \, \text{cm}^3 \).
Slant Height Calculation: \( l = \sqrt{10^2 + 3.464^2} \approx 10.54 \, \text{cm} \).
Conversions (Base Edge):
- \( \text{cm} = 4 \),
- \( \text{m} = 0.04 \),
- \( \text{in} \approx 1.575 \),
- \( \text{ft} \approx 0.131 \).
Conversions (Apothem):
- \( \text{cm} \approx 3.464 \),
- \( \text{m} \approx 0.0346 \),
- \( \text{in} \approx 1.364 \),
- \( \text{ft} \approx 0.114 \).
Conversions (Slant Height):
- \( \text{cm} \approx 10.54 \),
- \( \text{m} \approx 0.105 \),
- \( \text{in} \approx 4.15 \),
- \( \text{ft} \approx 0.346 \).
Conversions (Base Perimeter):
- \( \text{cm} = 24 \),
- \( \text{m} = 0.24 \),
- \( \text{in} \approx 9.449 \),
- \( \text{ft} \approx 0.787 \).
Conversions (Volume):
- \( \text{cm}^3 \approx 138.564 \),
- \( \text{m}^3 \approx 0.000139 \),
- \( \text{in}^3 \approx 8.454 \),
- \( \text{ft}^3 \approx 0.00489 \),
- \( \text{liters} \approx 0.139 \).

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