Total Surface Area Of Triakis Tetrahedron Given Volume Calculator

Formula Used:

\[ TSA = \frac{3}{5} \times \sqrt{11} \times \left( \frac{20 \times V}{3 \times \sqrt{2}} \right)^{\frac{2}{3}} \]

Total Surface Area of Triakis Tetrahedron:

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1. What is the Total Surface Area of Triakis Tetrahedron?

The Total Surface Area of a Triakis Tetrahedron is the total area of all its faces. A Triakis Tetrahedron is a polyhedron created by attaching a triangular pyramid to each face of a regular tetrahedron, resulting in a shape with 12 isosceles triangular faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{3}{5} \times \sqrt{11} \times \left( \frac{20 \times V}{3 \times \sqrt{2}} \right)^{\frac{2}{3}} \]

Where:

\( TSA \) — Total Surface Area (m²)
\( V \) — Volume of Triakis Tetrahedron (m³)
\( \sqrt{11} \) — Square root of 11
\( \sqrt{2} \) — Square root of 2

Explanation: This formula calculates the total surface area based on the volume of the Triakis Tetrahedron, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric shapes is fundamental in various fields including architecture, engineering, material science, and 3D modeling. It helps in determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the volume of the Triakis Tetrahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be obtained by adding a triangular pyramid to each face of a regular tetrahedron, resulting in a polyhedron with 12 faces.

Q2: Why is the formula so complex?
A: The formula involves geometric relationships between volume and surface area in three-dimensional space, requiring mathematical constants and exponents to accurately represent these relationships.

Q3: What are the units for the result?
A: The result is given in square meters (m²), which is the standard unit for surface area measurements.

Q4: Can this calculator handle very large or very small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by the precision of the computing system.

Q5: Is this formula applicable to all polyhedrons?
A: No, this specific formula is only valid for Triakis Tetrahedrons. Different polyhedrons have different formulas for calculating surface area from volume.