Volume Of Triakis Tetrahedron Given Midsphere Radius Calculator

Volume Of Triakis Tetrahedron Formula:

\[ V = \frac{3}{20} \times \sqrt{2} \times \left( \frac{4 \times r_m}{\sqrt{2}} \right)^3 \]

Volume of Triakis Tetrahedron:

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1. What is the Volume of Triakis Tetrahedron?

The Volume of Triakis Tetrahedron is the quantity of three dimensional space enclosed by the entire surface of Triakis Tetrahedron. It is calculated based on the midsphere radius using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{3}{20} \times \sqrt{2} \times \left( \frac{4 \times r_m}{\sqrt{2}} \right)^3 \]

Where:

\( V \) — Volume of Triakis Tetrahedron (m³)
\( r_m \) — Midsphere Radius of Triakis Tetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the volume of a Triakis Tetrahedron based on its midsphere radius, using geometric relationships and mathematical constants.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, and various scientific applications. It helps in understanding spatial properties and material requirements.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that is the dual of the truncated tetrahedron. It has 12 isosceles triangular faces.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of a sphere that is tangent to all edges of the polyhedron.

Q3: What are the units of measurement?
A: The calculator uses meters for input and cubic meters for volume output. Ensure consistent units for accurate results.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is designed only for calculating the volume of a Triakis Tetrahedron given its midsphere radius.

Q5: What is the accuracy of the calculation?
A: The calculator provides results with 4 decimal places precision, which is sufficient for most practical applications.