Volume Of Triakis Tetrahedron Given Total Surface Area Calculator

Formula Used:

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

Volume of Triakis Tetrahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 an important geometric measurement in three-dimensional space calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Triakis Tetrahedron (m³)
\( TSA \) — Total Surface Area of Triakis Tetrahedron (m²)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{11} \) — Square root of 11 (approximately 3.3166)

Explanation: This formula calculates the volume of a Triakis Tetrahedron based on its total surface area, using mathematical constants and geometric relationships.

3. Importance of Volume Calculation

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

4. Using the Calculator

Tips: Enter the total surface area of the Triakis Tetrahedron in square 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 seen as a tetrahedron with triangular pyramids added to each face.

Q2: What units should I use for the input?
A: The calculator expects the total surface area in square meters (m²) and returns volume in cubic meters (m³).

Q3: Can this formula be used for any Triakis Tetrahedron?
A: Yes, this formula applies to all regular Triakis Tetrahedrons where the ratio between the edge lengths of the tetrahedron and the added pyramids is constant.

Q4: What if I have the edge length instead of surface area?
A: You would need to use a different formula that calculates volume directly from edge length, as this calculator specifically uses surface area as input.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input value, using the exact geometric relationships defined by the formula.