Height of Elongated Pentagonal Bipyramid Given Surface to Volume Ratio Calculator

Formula Used:

\[ h = \left(2\sqrt{\frac{5-\sqrt{5}}{10}}+1\right) \times \frac{\frac{5\sqrt{3}}{2}+5}{\left(\frac{5+\sqrt{5}}{12}+\frac{\sqrt{25+10\sqrt{5}}}{4}\right) \times AV} \]

Height of Elongated Pentagonal Bipyramid:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Height of Elongated Pentagonal Bipyramid?

The Height of Elongated Pentagonal Bipyramid is the vertical distance from the highest point to the lowest point of the Elongated Pentagonal Bipyramid, a geometric solid formed by elongating a pentagonal bipyramid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \left(2\sqrt{\frac{5-\sqrt{5}}{10}}+1\right) \times \frac{\frac{5\sqrt{3}}{2}+5}{\left(\frac{5+\sqrt{5}}{12}+\frac{\sqrt{25+10\sqrt{5}}}{4}\right) \times AV} \]

Where:

\( h \) — Height of Elongated Pentagonal Bipyramid (m)
\( AV \) — SA:V of Elongated Pentagonal Bipyramid (1/m)

Explanation: The formula calculates the height based on the surface area to volume ratio of the elongated pentagonal bipyramid.

3. Importance of Height Calculation

Details: Calculating the height of geometric solids is important in various fields including architecture, engineering, and mathematical modeling, helping in understanding spatial dimensions and proportions.

4. Using the Calculator

Tips: Enter the surface area to volume ratio (SA:V) in 1/m. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is an Elongated Pentagonal Bipyramid?
A: An Elongated Pentagonal Bipyramid is a polyhedron formed by elongating a pentagonal bipyramid, resulting in a structure with pentagonal bases and triangular faces.

Q2: How is SA:V defined?
A: SA:V (Surface Area to Volume Ratio) is the ratio of the total surface area of a solid to its volume, important in various physical and biological contexts.

Q3: What units are used?
A: Height is measured in meters (m) and SA:V in reciprocal meters (1/m).

Q4: Are there limitations to this formula?
A: The formula is specific to the elongated pentagonal bipyramid geometry and assumes ideal geometric conditions.

Q5: Can this calculator be used for other shapes?
A: No, this calculator is specifically designed for elongated pentagonal bipyramids. Other shapes require different formulas.