The Dodecahedron Calculator is a specialized tool designed to compute key geometric properties of a dodecahedron based on the length of its edges. It simplifies calculations of surface area and volume, which are essential for various academic and professional applications in geometry, architecture, and design.
Formula of Dodecahedron Calculator
Surface Area of a Dodecahedron
The surface area A of a dodecahedron can be calculate using the following formula:
A = 3 * sqrt(25 + 10 * sqrt(5)) * a^2
Volume of a Dodecahedron
The volume V of a dodecahedron can be calculate with:
V = (15 + 7 * sqrt(5)) / 4 * a^3
Where:
- a is the edge length of the dodecahedron.
Pre-calculated Table for Common Edge Lengths
| Edge Length (cm) | Surface Area (cm²) | Volume (cm³) |
|---|---|---|
| 1 | 3 × sqrt(25 + 10 × sqrt(5)) × 1² | (15 + 7 × sqrt(5)) / 4 × 1³ |
| 2 | 3 × sqrt(25 + 10 × sqrt(5)) × 2² | (15 + 7 × sqrt(5)) / 4 × 2³ |
| 3 | 3 × sqrt(25 + 10 × sqrt(5)) × 3² | (15 + 7 × sqrt(5)) / 4 × 3³ |
| 4 | 3 × sqrt(25 + 10 × sqrt(5)) × 4² | (15 + 7 × sqrt(5)) / 4 × 4³ |
| 5 | 3 × sqrt(25 + 10 × sqrt(5)) × 5² | (15 + 7 × sqrt(5)) / 4 × 5³ |
Example of Dodecahedron Calculator
Let's consider a dodecahedron with an edge length of 5 cm. Using our calculator, the surface area and volume would be computed as follows:
- Surface Area: A = 3 * sqrt(25 + 10 * sqrt(5)) * (5)^2
- Volume: V = (15 + 7 * sqrt(5)) / 4 * (5)^3
These calculations illustrate the efficiency and accuracy of the Dodecahedron Calculator in practical scenarios.
Most Common FAQs
A dodecahedron is a three-dimensional shape with twelve flat faces, each being a regular pentagon.
Our calculator uses precise mathematical formulas to ensure high accuracy, suitable for academic and professional applications.
Yes, the calculator can process both decimal and fractional inputs, making it versatile for various use cases.