Volume of Truncated Rhombohedron given Circumsphere Radius Calculator

Volume of Truncated Rhombohedron Formula:

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

Volume of Truncated Rhombohedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Volume of Truncated Rhombohedron?

The Volume of Truncated Rhombohedron is the total quantity of three-dimensional space enclosed by the surface of the Truncated Rhombohedron. It represents the capacity or the amount of material that can be contained within this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the volume based on the circumsphere radius, incorporating mathematical constants and geometric relationships specific to the truncated rhombohedron shape.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in various fields including architecture, engineering, material science, and 3D modeling. It helps in determining capacity, material requirements, and spatial relationships.

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 precise mathematical formula.

5. Frequently Asked Questions (FAQ)

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

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: What units should I use for input?
A: The calculator uses meters as the unit for length measurements. Ensure consistent units for accurate results.

Q4: How accurate is this calculation?
A: The calculation uses precise mathematical formulas and provides results with high accuracy, typically rounded to 6 decimal places.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula is designed only for calculating the volume of a truncated rhombohedron given its circumsphere radius.