1. What is the Volume of Rhombohedron?

The volume of a rhombohedron is the total three-dimensional space enclosed by its six rhombus-shaped faces. It represents the capacity of this geometric solid.

2. How Does the Calculator Work?

The calculator uses the volume formula:

Where:

• \( V \) — Volume of Rhombohedron (m³)
• \( l_e \) — Edge Length of Rhombohedron (m)
• \( \angle_{\text{Obtuse}} \) — Obtuse Angle of Rhombohedron (radians)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \cos \) — Cosine trigonometric function
• \( \sqrt \) — Square root function

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

3. Importance of Volume Calculation

Details: Calculating the volume of a rhombohedron is essential in crystallography, material science, and geometric modeling where this shape frequently appears.

4. Using the Calculator

Tips: Enter the edge length in meters and the obtuse angle in degrees (must be between 90° and 180°). All values must be positive and valid.

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's a special case of a parallelepiped.

Q2: Why is the obtuse angle important?
A: The obtuse angle between adjacent edges determines the shape and proportions of the rhombohedron, directly affecting its volume calculation.

Q3: Can this calculator handle acute angles?
A: No, this specific formula is designed for the obtuse angle of the rhombohedron (angles greater than 90 degrees).

Q4: What are typical applications of rhombohedron volume calculations?
A: These calculations are used in crystallography, mineralogy, and materials science where many crystals form rhombohedral structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input parameters. The accuracy depends on the precision of the input values.