Regular Dodecahedron Volume Calculator
The dodecahedron volume calculator is a tool designed for mathematicians, educators, and students to quickly find the volume of a regular dodecahedron based on the given edge length. It simplifies the process by providing instant results and explanations.
Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da RechnerOnline.
The Formula Explained
The volume \( V \) of a regular dodecahedron with edge length \( a \) is given by:
\[ V = \frac{15 + 7\sqrt{5}}{4} \times a^3 \]
Glossary of Terms
- Edge Length (a): The length of one side of the dodecahedron.
- Volume (V): The space occupied by the dodecahedron.
Example Calculation
For an edge length of 2 units, the volume is calculated as follows:
\( V = \frac{15 + 7\sqrt{5}}{4} \times 2^3 \approx 61.30 \) cubic units.
Frequently Asked Questions (FAQ)
What is a regular dodecahedron?
A regular dodecahedron is a three-dimensional shape with twelve equal pentagonal faces, twenty vertices, and thirty edges.
How is the volume formula derived?
The volume formula is derived using advanced geometric principles and the golden ratio.
Can this calculator be used for irregular dodecahedrons?
No, this calculator is specifically designed for regular dodecahedrons.
How accurate is this calculator?
This calculator uses precise mathematical formulas to ensure accuracy.
Why is the edge length required?
The edge length is necessary because the volume of a dodecahedron is directly proportional to the cube of its edge length.