Calcular el volumen del dodecaedro

Dada la arista del dodecaedro, calcule su volumen. El volumen es la cantidad de espacio que ocupan las formas. 
Un dodecaedro es una figura tridimensional formada por 12 caras o lados planos. Todas las caras son pentágonos del mismo tamaño. La palabra ‘dodecaedro’ proviene de las palabras griegas dodeca (‘doce’) y hedron (‘caras’).
Fórmula: 
Volumen = (15 + 7√5)*e 3/4 Donde ^e
es la longitud de una arista.
Ejemplos: 
 

Input : side = 4
Output : 490.44

Input : side = 9
Output : 5586.41

// CPP program to calculate
// Volume of dodecahedron
#include <bits/stdc++.h>
using namespace std;
 
// utility Function
double vol_of_dodecahedron(int side)
{
    return (((15 + (7 * (sqrt(5)))) / 4)
                       * (pow(side, 3))) ;
}
// Driver Function
int main()
{
    int side = 4;
     
    cout << "Volume of dodecahedron = "
         << vol_of_dodecahedron(side);
}

// Java program to calculate
// Volume of dodecahedron
 
import java.io.*;
 
class GFG
{
        // driver function
    public static void main (String[] args)
       {
           int side = 4;
           System.out.print("Volume of dodecahedron = ");
           System.out.println(vol_of_dodecahedron(side));
       }
     
     static double vol_of_dodecahedron(int side)
        {
             return (((15 + (7 * (Math.sqrt(5)))) / 4)
                       * (Math.pow(side, 3)));
        }
}
 
// This code is contributed
// by Azkia Anam.

# Python3 program to calculate
# Volume of dodecahedron
import math
 
# utility Function
def vol_of_dodecahedron(side) :
 
    return (((15 + (7 * (math.sqrt(5)))) / 4)
                    * (math.pow(side, 3)))
 
# Driver Function
side = 4
print("Volume of dodecahedron =",
       round(vol_of_dodecahedron(side), 2))
        
# This code is contributed by Smitha Dinesh Semwal

// C# program to calculate
// Volume of dodecahedron
using System;
 
public class GFG
{
     
    // utility Function
    static float vol_of_dodecahedron(int side)
    {
        return (float)(((15 + (7 * (Math.Sqrt(5)))) / 4)
                        * (Math.Pow(side, 3))) ;
    }
     
     
    // Driver Function
    static public void Main ()
    {
        int side = 4;
     
        Console.WriteLine("Volume of dodecahedron = "
            + vol_of_dodecahedron(side));
    }
}
 
/* This code is contributed by vt_m.*/

<?php
// PHP program to calculate
// Volume of dodecahedron
 
// utility Function
function vol_of_dodecahedron($side)
{
    return (((15 + (7 * (sqrt(5)))) / 4)
                      * (pow($side, 3))) ;
}
 
    // Driver Function
    $side = 4;
    echo ("Volume of dodecahedron = ");
    echo(vol_of_dodecahedron($side));
     
// This code is contributed by vt_m.
?>

<script>
// javascript program to calculate
// Volume of dodecahedron
 
 
// utility Function
function vol_of_dodecahedron( side)
{
    return (((15 + (7 * (Math.sqrt(5)))) / 4)
                       * (Math.pow(side, 3))) ;
}
 
// Driver Function
    let side = 4;
    document.write("Volume of dodecahedron = " +
    vol_of_dodecahedron(side).toFixed(2));
     
    // This code contributed by gauravrajput1
</script>

Producción : 
 

 
Volume of dodecahedron = 490.44

Complejidad de tiempo: O(logn) 
Espacio auxiliar: O(1)