How To Find Volume of Dodecahedron in Java?

A dodecahedron is a three-dimensional shape that has twelve flat faces. It is derived from two Greek words, i.e., 'dodeka', which means 12, and 'hedra', which means face. In other words, a dodecahedron is a special type of polyhedron that has 12 faces.

To make a dodecahedron, you can use the 12 pyramids and the base as a pentagon. Following diagram will provide a better understanding of its shape and edges:

Where a is the length of the edge.

Volume of Dodecahedron

A dodecahedron volume refers to the amount of space occupied by this 3D shape, which has 12 faces. To calculate the volume of a dodecahedron in mathematics, we have a formula:

$$\mathrm{Volume \:=\: (15\: +\: 7\sqrt{5})*a^3/4}$$

Where, a refers to the length of one edge of the dodecahedron.

Input & Output Scenarios

Below are a few input and output scenarios that provide a clear understanding of how to calculate the volume of the dodecahedron:

Scenario 1

Suppose the given edge length is 4:

Input: 4
Output: 490.44

Calculation: Volume = (15 + 7\sqrt{5}) x (4 x 4 x 4)/4 = 30.65 x 16 = 490.44

Scenario 2

Suppose the input edge length is 3:

Input: 3
Output: 206.206.89

Calculation: Volume = (15 + 7\sqrt{5}) x (3 x 3 x 3)/4 = 30.65 x 6.75 = 206.89

Let's see the program along with its output one by one.

Example 1

The following example calculates the volume of the dodecahedron, for which the edge length is given as 4, using the above volume formula:

public class Volume {
   public static void main(String args[]){
      double edege_length = 5.5;
      System.out.println("The edge length of dodecahedron: " + edege_length);
      
      //calculate volume using formula
      double volume= (((15 + (7 * (Math.sqrt(5)))) / 4) * (Math.pow(edege_length, 3)));
      System.out.println("The volume of dodecahedron: " + volume);
   }
}

Following is the output of the above program:

The edge length of dodecahedron: 5.5
The volume of dodecahedron: 1274.9514170739233

Example 2

In the example below, we define a function named calculateVolume(), which calculates the volume of the dodecahedron and returns it with the help of its edge length, i.e., 6, using the above formula:

public class Volume {
   //method to calculate the dodecahedron volume
   public static double calculateVolume(double a){
      //using the formula to calculate volume
      double volume = (((15 + (7 * (Math.sqrt(5)))) / 4) * (Math.pow(a, 3)));
      return volume;
   }
   public static void main(String args[]){
      double edge_length = 6;
      System.out.println("The length of edge: " + edge_length);
      
      //calling the calculateVolume() method to find the dodecahedron volume
      System.out.println("The volume of the dodecahedron is: " + calculateVolume(edge_length));
   }
}

The above program produces the following output:

The length of edge: 6.0
The volume of the dodecahedron is: 1655.2336954949205