Volume Of Stellated Octahedron Given Circumsphere Radius Calculator

Formula Used:

\[ V = \frac{\sqrt{2}}{8} \times \left( \frac{4 \times r_c}{\sqrt{6}} \right)^3 \]

Volume of Stellated Octahedron:

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1. What is 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 or the amount of space that the solid occupies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{2}}{8} \times \left( \frac{4 \times r_c}{\sqrt{6}} \right)^3 \]

Where:

\( V \) — Volume of Stellated Octahedron (m³)
\( r_c \) — Circumsphere Radius of Stellated Octahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{6} \) — Square root of 6 (approximately 2.4495)

Explanation: The formula calculates the volume of a stellated octahedron based on its circumsphere radius, using mathematical constants and geometric relationships.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, engineering, architecture, and 3D modeling. It helps in understanding spatial properties and capacity requirements.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the volume using the mathematical formula.

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 solid.

Q2: What is Circumsphere Radius?
A: Circumsphere radius is the radius of the sphere that contains the polyhedron in such a way that all the vertices are lying on the sphere.

Q3: Why is the formula structured this way?
A: The formula derives from the geometric relationships between the circumsphere radius and the volume of the stellated octahedron, using mathematical constants specific to this shape.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula. The accuracy depends on the precision of the input value provided.