General Pyramid Volume Calculator

Base Shape:

Side Length \( a \):

Height \( h \):

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

1. What is a Pyramid Volume Calculator?

Definition: This calculator computes the volume of a general pyramid with a regular-shaped base, using the base area and height.

Purpose: Useful for geometric calculations in mathematics, architecture, and engineering.

2. How Does the Calculator Work?

The calculation is based on the following steps:

\[ \text{Base Area} = \frac{n \times a^2}{4 \times \tan\left(\frac{\pi}{n}\right)} \]

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Where \( n \) is the number of sides of the base, \( a \) is the side length, and \( h \) is the height.

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48)
Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001)

Explanation: Inputs are converted to cm, the base area is calculated based on the number of sides, and the volume is computed in cm³, then converted to in³, ft³, and m³.

3. Importance of Pyramid Volume Calculation

Details: Calculating the volume of a pyramid is essential in architecture, engineering, and historical studies (e.g., the Great Pyramid of Giza).

4. Using the Calculator

Tips: Select the base shape (3 to 100 sides), then enter the side length \( a \) and height \( h \) in mm, cm, m, in, or ft (all >0). Results show the volume in cm³, in³, ft³, and m³.

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