Total Surface Area of Elongated Triangular Bipyramid given Surface to Volume Ratio Calculator

Formula Used:

\[ TSA = \frac{3}{2} \times (2+\sqrt{3}) \times \left( \frac{\frac{3}{2} \times (2+\sqrt{3})}{\frac{(2\sqrt{2})+(3\sqrt{3})}{12} \times SA:V} \right)^2 \]

Total Surface Area (TSA):

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1. What is the Elongated Triangular Bipyramid?

The Elongated Triangular Bipyramid is a polyhedron formed by elongating a triangular bipyramid. It consists of 6 equilateral triangles and 3 squares, making it a Johnson solid (J14).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{3}{2} \times (2+\sqrt{3}) \times \left( \frac{\frac{3}{2} \times (2+\sqrt{3})}{\frac{(2\sqrt{2})+(3\sqrt{3})}{12} \times SA:V} \right)^2 \]

Where:

\( TSA \) — Total Surface Area (m²)
\( SA:V \) — Surface to Volume Ratio (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the total surface area based on the given surface to volume ratio of the elongated triangular bipyramid.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is important in various fields including architecture, materials science, and engineering for determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Johnson solid?
A: Johnson solids are convex polyhedra with regular faces that are not uniform (unlike Platonic or Archimedean solids).

Q2: How many faces does an elongated triangular bipyramid have?
A: It has 9 faces - 6 equilateral triangles and 3 squares.

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, nanotechnology, and architectural design where precise surface area measurements are required.

Q4: Are there limitations to this formula?
A: This formula is specific to the elongated triangular bipyramid shape and assumes perfect geometric proportions.

Q5: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating point precision.