Volume of Hollow Pyramid Calculator

Volume of Hollow Pyramid Formula:

\[ V = \frac{\frac{1}{3} \times n \times h_{Inner} \times l_{e(Base)}^2}{4 \times \tan\left(\frac{\pi}{n}\right)} \]

Number of Base Vertices of Hollow Pyramid:

vertices

Inner Height of Hollow Pyramid:

Edge Length of Base of Hollow Pyramid:

Volume of Hollow Pyramid:

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1. What is the Volume of Hollow Pyramid?

The Volume of Hollow Pyramid represents the total three-dimensional space enclosed by the surface of a hollow pyramid structure, which consists of an outer pyramid with an inner pyramid removed from it.

2. How Does the Calculator Work?

The calculator uses the Hollow Pyramid volume formula:

\[ V = \frac{\frac{1}{3} \times n \times h_{Inner} \times l_{e(Base)}^2}{4 \times \tan\left(\frac{\pi}{n}\right)} \]

Where:

\( V \) — Volume of Hollow Pyramid (m³)
\( n \) — Number of Base Vertices of Hollow Pyramid
\( h_{Inner} \) — Inner Height of Hollow Pyramid (m)
\( l_{e(Base)} \) — Edge Length of Base of Hollow Pyramid (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \tan \) — Trigonometric tangent function

Explanation: The formula calculates the volume of a hollow pyramid by considering the geometric properties of the base polygon and the inner height of the structure.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for architectural design, material estimation, structural analysis, and various engineering applications involving pyramid-shaped hollow structures.

4. Using the Calculator

Tips: Enter the number of base vertices (minimum 3), inner height in meters, and edge length of base in meters. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the minimum number of base vertices required?
A: The minimum number of base vertices is 3, which corresponds to a triangular base pyramid.

Q2: Can this formula be used for any regular polygon base?
A: Yes, the formula works for any regular polygon base with 3 or more sides.

Q3: What units should be used for input values?
A: Height and edge length should be in consistent units (typically meters), and the volume result will be in cubic units of the same measurement.

Q4: Are there limitations to this formula?
A: The formula assumes a regular polygon base and requires the inner height to be properly measured from the apex to the base plane.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric shapes with the given parameters.