Missing Height of Hollow Pyramid Given Volume Calculator

Formula Used:

\[ h_{Missing} = h_{Total} - \frac{12 \times V \times \tan(\pi/n)}{n \times l_e(Base)^2} \]

Total Height of Hollow Pyramid:

Volume of Hollow Pyramid:

m³

Number of Base Vertices:

Edge Length of Base:

Missing Height of Hollow Pyramid:

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1. What is Missing Height of Hollow Pyramid?

The Missing Height of Hollow Pyramid is the length of the perpendicular from the apex of the removed pyramid to the base of the removed pyramid in the Hollow Pyramid structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ h_{Missing} = h_{Total} - \frac{12 \times V \times \tan(\pi/n)}{n \times l_e(Base)^2} \]

Where:

\( h_{Missing} \) — Missing Height of Hollow Pyramid (m)
\( h_{Total} \) — Total Height of Hollow Pyramid (m)
\( V \) — Volume of Hollow Pyramid (m³)
\( n \) — Number of Base Vertices
\( l_e(Base) \) — Edge Length of Base (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \tan \) — Trigonometric tangent function

Explanation: This formula calculates the missing height by considering the total height, volume, number of base vertices, and base edge length of the hollow pyramid structure.

3. Importance of Missing Height Calculation

Details: Calculating the missing height is crucial for architectural design, geometric analysis, and structural engineering applications involving hollow pyramid structures.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow pyramid?
A: A hollow pyramid is a pyramid structure with a smaller pyramid removed from its interior, creating a hollow space within.

Q2: Why is the tangent function used in this formula?
A: The tangent function relates the angles of the pyramid's faces to its dimensional properties, making it essential for calculating missing heights.

Q3: 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.

Q4: Can this calculator handle different units?
A: The calculator uses meters for length measurements and cubic meters for volume. Convert other units to these before calculation.

Q5: What if I get a negative result for missing height?
A: A negative result indicates that the input values may be inconsistent or that the calculated missing height exceeds the total height, which is physically impossible. Please verify your input values.