Volume Of Stellated Octahedron Given Total Surface Area Calculator

Formula Used:

\[ V = \frac{\sqrt{2}}{8} \times \left( \frac{2 \times TSA}{3 \times \sqrt{3}} \right)^{\frac{3}{2}} \]

Volume of Stellated Octahedron:

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1. What is the Volume of Stellated Octahedron?

The Volume of Stellated Octahedron is the total quantity of three dimensional space enclosed by the surface of the Stellated Octahedron. It represents the capacity of this geometric shape in three-dimensional space.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{2}}{8} \times \left( \frac{2 \times TSA}{3 \times \sqrt{3}} \right)^{\frac{3}{2}} \]

Where:

\( V \) — Volume of Stellated Octahedron (m³)
\( TSA \) — Total Surface Area of Stellated Octahedron (m²)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{3} \) — Square root of 3 (approximately 1.7321)

Explanation: This formula calculates the volume of a stellated octahedron based on its total surface area, using mathematical relationships between surface area and volume for this specific geometric shape.

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, material requirements, and structural properties of three-dimensional objects.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a stellated octahedron?
A: A stellated octahedron is a polyhedron created by extending the faces of a regular octahedron until they meet again, forming a star-shaped three-dimensional figure.

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

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the stellated octahedron geometry only. Other polyhedra have different volume-surface area relationships.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications.

Q5: Are there any limitations to this calculation?
A: The formula assumes a perfect geometric shape. For real-world applications, additional factors such as material thickness and manufacturing tolerances may need to be considered.