Surface To Volume Ratio Of Hollow Pyramid Given Inner Height And Missing Height Calculator

Surface To Volume Ratio Of Hollow Pyramid Formula:

\[ \text{Surface to Volume Ratio} = \frac{n \cdot l_{base}/2 \cdot \left( \sqrt{(h_{inner} + h_{missing})^2 + \left( \frac{l_{base}^2}{4} \cdot \cot^2\left(\frac{\pi}{n}\right) \right)} + \sqrt{h_{missing}^2 + \left( \frac{l_{base}^2}{4} \cdot \cot^2\left(\frac{\pi}{n}\right) \right)} \right)}{\frac{1}{3} \cdot n \cdot h_{inner} \cdot \frac{l_{base}^2}{4 \cdot \tan\left(\frac{\pi}{n}\right)}} \]

Number of Base Vertices (n):

Edge Length of Base (l_base):

Inner Height (h_inner):

Missing Height (h_missing):

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Hollow Pyramid?

The Surface to Volume Ratio of a Hollow Pyramid is the numerical ratio of the total surface area to the volume of the hollow pyramid structure. It represents how much surface area is available per unit volume of the pyramid.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( n \) — Number of base vertices
\( l_{base} \) — Edge length of base (m)
\( h_{inner} \) — Inner height (m)
\( h_{missing} \) — Missing height (m)
\( \pi \) — Archimedes' constant (≈3.14159)

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various engineering and architectural applications, particularly in heat transfer, mass transfer, and structural efficiency analysis of hollow pyramid structures.

4. Using the Calculator

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

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 surface to volume ratio important?
A: It indicates how efficiently a structure can exchange heat or materials with its environment, which is critical in thermal and chemical engineering applications.

Q3: What are typical values for surface to volume ratio?
A: The ratio varies significantly based on dimensions, but generally ranges from 0.1 to 10 m⁻¹ for most practical pyramid structures.

Q4: Can this calculator handle different base shapes?
A: Yes, the calculator works for regular polygonal bases with any number of vertices (minimum 3 for triangular base).

Q5: What units should I use?
A: Use consistent units (preferably meters) for all length measurements to get accurate results in m⁻¹.