Surface To Volume Ratio Of Rhombohedron Given Obtuse Angle Calculator

Surface to Volume Ratio of Rhombohedron Formula:

\[ \text{Surface to Volume Ratio} = \frac{6 \times \sin(\pi - \angle_{\text{Obtuse}})}{l_e \times (1 - \cos(\pi - \angle_{\text{Obtuse}})) \times \sqrt{1 + 2 \times \cos(\pi - \angle_{\text{Obtuse}})}} \]

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Rhombohedron?

The Surface to Volume Ratio of a Rhombohedron is the numerical ratio of the total surface area to the volume of the Rhombohedron. It's an important geometric property that indicates how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( \angle_{\text{Obtuse}} \) — Obtuse angle of the rhombohedron (in radians)
\( l_e \) — Edge length of the rhombohedron
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the surface to volume ratio based on the obtuse angle and edge length of the rhombohedron, using trigonometric functions to account for the geometric relationships.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. It affects properties like heat transfer, reaction rates, and structural efficiency. For rhombohedrons, this ratio helps understand how the shape's geometry influences its surface area relative to its volume.

4. Using the Calculator

Tips: Enter the obtuse angle in degrees (must be between 90° and 180°) and the edge length in meters. Both values must be positive numbers with the angle strictly between 90 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a rhombohedron?
A: A rhombohedron is a three-dimensional figure with six rhombus-shaped faces. All edges have equal length, and opposite faces are parallel.

Q2: Why is the obtuse angle important in this calculation?
A: The obtuse angle determines the shape and proportions of the rhombohedron, which directly affects both the surface area and volume calculations.

Q3: What are typical values for surface to volume ratio?
A: The ratio depends on the specific dimensions of the rhombohedron. Smaller rhombohedrons generally have higher surface to volume ratios, while larger ones have lower ratios.

Q4: Can this formula be used for acute angles?
A: No, this specific formula is designed for the obtuse angle of the rhombohedron. Different formulas would be needed for acute angles or other geometric parameters.

Q5: What units does the calculator use?
A: The calculator uses degrees for angles and meters for length, with the result in meters⁻¹ (inverse meters).