Volume Of Rhombicosidodecahedron Given Total Surface Area Calculator

Formula Used:

\[ V = \frac{60 + 29\sqrt{5}}{3} \times \left( \sqrt{ \frac{TSA}{30 + 5\sqrt{3} + 3\sqrt{25 + 10\sqrt{5}}} } \right)^3 \]

Volume of Rhombicosidodecahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Rhombicosidodecahedron?

The Rhombicosidodecahedron is an Archimedean solid with 20 regular triangular faces, 30 square faces, and 12 regular pentagonal faces. Its volume represents the total three-dimensional space enclosed by its surface.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{60 + 29\sqrt{5}}{3} \times \left( \sqrt{ \frac{TSA}{30 + 5\sqrt{3} + 3\sqrt{25 + 10\sqrt{5}}} } \right)^3 \]

Where:

\( V \) — Volume of Rhombicosidodecahedron (m³)
\( TSA \) — Total Surface Area (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula derives the volume from the total surface area using the geometric properties and mathematical relationships specific to the Rhombicosidodecahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, architecture, and various scientific fields for understanding spatial relationships and material requirements.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding volume.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicosidodecahedron?
A: It's one of the 13 Archimedean solids, characterized by its combination of triangular, square, and pentagonal faces in a specific arrangement.

Q2: Why is this formula so complex?
A: The complexity arises from the intricate geometry of the Rhombicosidodecahedron, which requires mathematical expressions involving square roots and constants derived from its specific proportions.

Q3: What are the practical applications of this calculation?
A: This calculation is used in mathematical modeling, architectural design, material science, and educational contexts where understanding geometric properties is important.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombicosidodecahedron. Other polyhedra have their own unique volume formulas.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Rhombicosidodecahedron. The accuracy depends on the precision of the input surface area value.