Total Surface Area of Rhombohedron given Volume Calculator

Formula Used:

\[ TSA = 6 \times \left( \frac{V}{(1 - \cos(\angle_{Acute})) \times \sqrt{1 + 2 \times \cos(\angle_{Acute})}} \right)^{2/3} \times \sin(\angle_{Acute}) \]

Total Surface Area of Rhombohedron (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Total Surface Area of Rhombohedron?

The Total Surface Area of Rhombohedron is the total quantity of plane enclosed on the entire surface of the Rhombohedron. It represents the sum of the areas of all six rhombus faces that make up the rhombohedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 6 \times \left( \frac{V}{(1 - \cos(\angle_{Acute})) \times \sqrt{1 + 2 \times \cos(\angle_{Acute})}} \right)^{2/3} \times \sin(\angle_{Acute}) \]

Where:

\( TSA \) — Total Surface Area of Rhombohedron (m²)
\( V \) — Volume of Rhombohedron (m³)
\( \angle_{Acute} \) — Acute Angle of Rhombohedron (radians)

Explanation: This formula calculates the total surface area based on the volume and the acute angle between adjacent edges of the rhombohedron, using trigonometric functions to account for the geometric properties.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, heat transfer calculations, and structural analysis in engineering and architectural designs involving rhombohedral shapes.

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, and the volume must be a positive value for accurate results.

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. All edges have equal length, and opposite faces are parallel.

Q2: Why is the acute angle important in this calculation?
A: The acute angle determines the shape and proportions of the rhombohedron, affecting both its volume and surface area relationships.

Q3: Can this formula be used for any rhombohedron?
A: Yes, this formula applies to all rhombohedrons where all edges are equal in length and all faces are congruent rhombuses.

Q4: What are the units for the inputs and outputs?
A: Volume should be in cubic meters, angle in degrees, and the resulting surface area will be in square meters.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of rhombohedrons, provided accurate input values are given.