Surface to Volume Ratio of Elongated Pentagonal Bipyramid given Height Calculator

Formula Used:

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

Surface to Volume Ratio (SA:V):

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1. What is Surface to Volume Ratio of Elongated Pentagonal Bipyramid?

The surface to volume ratio (SA:V) of an elongated pentagonal bipyramid is a geometric measurement that compares the total surface area to the volume of this specific polyhedron. It's an important parameter in various scientific and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h \) — Height of the elongated pentagonal bipyramid (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the ratio by dividing the total surface area by the volume of the elongated pentagonal bipyramid, considering its specific geometric properties.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in materials science, chemistry, and physics as it affects properties like reactivity, heat transfer, and strength-to-weight ratios in structures with this geometric form.

4. Using the Calculator

Tips: Enter the height of the elongated pentagonal bipyramid in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated pentagonal bipyramid?
A: It's a polyhedron formed by elongating a pentagonal bipyramid by inserting a pentagonal prism between its two halves.

Q2: What units are used for the surface to volume ratio?
A: The ratio is expressed in reciprocal meters (m⁻¹), as it represents area divided by volume.

Q3: How does height affect the surface to volume ratio?
A: As height increases, the surface to volume ratio typically decreases, following the general principle that larger objects have smaller surface area relative to their volume.

Q4: What are practical applications of this calculation?
A: This calculation is useful in nanotechnology, crystallography, and architectural design where this specific geometric form is employed.

Q5: Are there limitations to this formula?
A: The formula assumes a perfect geometric shape with uniform dimensions and may not account for real-world imperfections or variations.