Edge Length of Rhombohedron given Volume Calculator

Formula Used:

\[ l_e = \left( \frac{V}{(1-\cos(\theta_{\text{acute}})) \cdot \sqrt{1+2\cos(\theta_{\text{acute}})}} \right)^{\frac{1}{3}} \]

Edge Length of Rhombohedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Edge Length of Rhombohedron?

The edge length of a rhombohedron is the distance between any pair of adjacent vertices of the polyhedron. It is a fundamental geometric property that helps define the size and proportions of the rhombohedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \left( \frac{V}{(1-\cos(\theta_{\text{acute}})) \cdot \sqrt{1+2\cos(\theta_{\text{acute}})}} \right)^{\frac{1}{3}} \]

Where:

\( l_e \) — Edge Length of Rhombohedron (m)
\( V \) — Volume of Rhombohedron (m³)
\( \theta_{\text{acute}} \) — Acute Angle of Rhombohedron (degrees)
\( \cos \) — Cosine trigonometric function
\( \sqrt \) — Square root function

Explanation: This formula calculates the edge length based on the volume and the acute angle between the edges of the rhombohedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties of rhombohedrons, which are important in crystallography, materials science, and various engineering applications.

4. Using the Calculator

Tips: Enter the volume in cubic meters and the acute angle in degrees. The angle must be between 0 and 90 degrees (exclusive), and the volume must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a rhombohedron?
A: A rhombohedron is a three-dimensional figure with six faces, each of which is a rhombus. It is a special case of a parallelepiped.

Q2: Why is the acute angle important in this calculation?
A: The acute angle determines the shape and proportions of the rhombohedron, affecting how the volume relates to the edge length.

Q3: Can this formula be used for any rhombohedron?
A: Yes, this formula applies to all rhombohedrons where all edges are of equal length and all angles between edges are equal.

Q4: What units should I use for input values?
A: Volume should be in cubic meters and angle in degrees. The calculator will output edge length in meters.

Q5: What if I get an undefined result?
A: An undefined result typically occurs when the denominator becomes zero, which happens when the acute angle approaches 0 degrees. Ensure the angle is properly within the valid range.