1. What is Volume of Octahedron given Insphere Radius?

The volume of an octahedron given its insphere radius is the total three-dimensional space enclosed by the surface of the octahedron, calculated using the relationship between the volume and the radius of the inscribed sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Octahedron (m³)
• \( r_i \) — Insphere Radius of Octahedron (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula directly relates the volume of a regular octahedron to the radius of its inscribed sphere through a cubic relationship.

3. Importance of Volume Calculation

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

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and valid. The calculator will compute the volume using the mathematical relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octahedron?
A: A regular octahedron is a polyhedron with eight equilateral triangular faces, twelve edges, and six vertices.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be inscribed within the octahedron, touching all faces.

Q3: Can this formula be used for irregular octahedrons?
A: No, this formula applies only to regular octahedrons where all faces are equilateral triangles and all edges are equal.

Q4: What are the units of measurement?
A: The insphere radius should be in meters (m), and the resulting volume will be in cubic meters (m³). Consistent units must be used.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octahedrons, though practical measurements may introduce some error.