Volume Of Gyrobifastigium Given Total Surface Area Calculator

Formula Used:

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

Volume of Gyrobifastigium:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Gyrobifastigium?

The volume of Gyrobifastigium is the total quantity of three-dimensional space enclosed by the surface of this Johnson solid. It is a polyhedron formed by attaching two triangular prisms base-to-base with a 90-degree rotation.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Gyrobifastigium (m³)
\( TSA \) — Total Surface Area of Gyrobifastigium (m²)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula calculates the volume based on the total surface area by first determining the edge length and then applying the volume formula for Gyrobifastigium.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and architecture. For Gyrobifastigium specifically, understanding its volume properties helps in material estimation and structural analysis applications.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding volume.

5. Frequently Asked Questions (FAQ)

Q1: What is a Gyrobifastigium?
A: Gyrobifastigium is a Johnson solid (J26) formed by attaching two triangular prisms base-to-base with a 90-degree rotation. It has 8 faces: 4 equilateral triangles and 4 squares.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and proper implementation of the formula.

Q3: Can this formula be used for any Gyrobifastigium?
A: Yes, this formula applies to all regular Gyrobifastigium shapes where all edges are equal in length.

Q4: What are the units of measurement?
A: The calculator uses meters for length, square meters for area, and cubic meters for volume. You can convert from other units as needed.

Q5: Are there other ways to calculate the volume?
A: Yes, the volume can also be calculated directly from the edge length using the formula: \( V = \frac{\sqrt{3}}{2} \times a^3 \), where a is the edge length.