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

**What is a dodecahedron?**

A dodecahedron is a three-dimensional shape with twelve flat faces, each being a regular pentagon.

**How accurate is the Dodecahedron Calculator?**

Our calculator uses precise mathematical formulas to ensure high accuracy, suitable for academic and professional applications.

**Can the calculator handle decimal or fractional edge lengths?**

Yes, the calculator can process both decimal and fractional inputs, making it versatile for various use cases.