Total Surface Area Of Hollow Pyramid Given Inner Height And Missing Height Calculator

Formula Used:

\[ TSA = \frac{n \times l_e}{2} \times \left( \sqrt{(h_{Inner} + h_{Missing})^2 + \left( \frac{l_e^2}{4} \times \cot^2\left(\frac{\pi}{n}\right) \right)} + \sqrt{h_{Missing}^2 + \left( \frac{l_e^2}{4} \times \cot^2\left(\frac{\pi}{n}\right) \right)} \right) \]

Number of Base Vertices (n):

Edge Length of Base (lₑ):

Inner Height (h_Inner):

Missing Height (h_Missing):

Total Surface Area (TSA):

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1. What is Total Surface Area of Hollow Pyramid?

The Total Surface Area of a Hollow Pyramid is the total amount of two-dimensional space occupied by all the faces of the pyramid, including both the outer and inner surfaces. It represents the complete surface coverage of the hollow geometric structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

\( n \) — Number of base vertices
\( l_e \) — Edge length of base (m)
\( h_{Inner} \) — Inner height (m)
\( h_{Missing} \) — Missing height (m)
\( \pi \) — Mathematical constant (3.14159)
\( \cot \) — Cotangent trigonometric function

Explanation: The formula calculates the combined surface area by considering the geometric properties of both the complete pyramid and the removed portion.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, structural analysis, cost calculation in construction, and understanding the geometric properties of hollow pyramid structures.

4. Using the Calculator

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

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 the larger pyramid.

Q2: Why is the number of base vertices important?
A: The number of vertices determines the polygonal base shape and affects the trigonometric calculations in the surface area formula.

Q3: What are typical applications of this calculation?
A: This calculation is used in architecture, engineering, 3D modeling, and manufacturing where hollow pyramid structures are employed.

Q4: How accurate is this calculation?
A: The calculation provides theoretical accuracy based on mathematical principles, though real-world applications may require additional considerations for material thickness and construction tolerances.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters before input, then convert the result back to your desired unit system.