Circumsphere Radius of Truncated Rhombohedron given Volume Calculator

Formula Used:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \left( \frac{3V}{5\sqrt{\sqrt{5} - 2}} \right)^{\frac{1}{3}} \]

Circumsphere Radius of Truncated Rhombohedron (r_c):

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1. What is Circumsphere Radius of Truncated Rhombohedron?

The Circumsphere Radius of a Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere. It is an important geometric property in three-dimensional space.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \left( \frac{3V}{5\sqrt{\sqrt{5} - 2}} \right)^{\frac{1}{3}} \]

Where:

\( r_c \) — Circumsphere Radius of Truncated Rhombohedron (m)
\( V \) — Volume of Truncated Rhombohedron (m³)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the circumsphere radius based on the volume of the truncated rhombohedron, using mathematical constants and operations.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is crucial for understanding the spatial properties and geometric constraints of truncated rhombohedrons in various applications including crystallography, material science, and 3D modeling.

4. Using the Calculator

Tips: Enter the volume of the truncated rhombohedron in cubic meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Rhombohedron?
A: A truncated rhombohedron is a polyhedron obtained by truncating the vertices of a rhombohedron, resulting in a shape with both triangular and hexagonal faces.

Q2: What are typical values for circumsphere radius?
A: The circumsphere radius depends on the volume of the truncated rhombohedron. Larger volumes will result in larger circumsphere radii.

Q3: What units should be used for volume input?
A: Volume should be entered in cubic meters (m³) for consistent results with the formula.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric truncated rhombohedron shape and may not apply to irregular or distorted forms.

Q5: Can this formula be used for other polyhedrons?
A: No, this specific formula is derived for truncated rhombohedrons only. Other polyhedrons have different formulas for calculating circumsphere radius.