1. What is the Volume of Octahedron Formula?

The volume of an octahedron can be calculated using the circumsphere radius with the formula: \( V = \frac{4 \times r_c^3}{3} \), where \( r_c \) is the circumsphere radius of the octahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Octahedron (m)

Explanation: This formula calculates the volume of a regular octahedron based on the radius of the sphere that circumscribes it, touching all its vertices.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes like octahedrons is essential in various fields including architecture, engineering, and 3D modeling for determining space occupancy and material requirements.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumsphere radius?
A: The circumsphere radius is the radius of the sphere that passes through all vertices of the octahedron.

Q2: Can this formula be used for irregular octahedrons?
A: No, this formula applies only to regular octahedrons where all faces are equilateral triangles.

Q3: What are the units for volume calculation?
A: The volume is calculated in cubic meters (m³) when the radius is provided in meters.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for regular octahedrons when the correct radius value is provided.

Q5: Can I calculate the radius from the volume?
A: Yes, the formula can be rearranged to \( r_c = \sqrt[3]{\frac{3V}{4}} \) to find the circumsphere radius from a given volume.