Volume of cube using its space diagonal

Given the length of space diagonal of a cube as d. The task is to calculate the volume occupied by the cube with the given length of space diagonal. Space diagonal is a line connecting two vertices that are not on the same face.

Examples:

Input: d = 5 
Output: Volume of Cube: 24.0563

Input: d = 10
Output: Volume of Cube: 192.45

Volume of cube whose space diagonal is given: 

Proof:

Let d = the length of diagonal |AB| and 
let a = the length of each side of the cube. 
Pythagoras #1 in triangle ACD: 

Pythagoras #2 in triangle ABC: 

Now we can solve for a in terms of d: 

This means that the volume V is: 

Below is the required implementation: 

C++

// C++ program to find the volume occupied
// by Cube with given space diagonal
#include <bits/stdc++.h>
using namespace std;

// Function to calculate Volume
float CubeVolume(float d)
{
    float Volume;

    // Formula to find Volume
    Volume = (sqrt(3) * pow(d, 3)) / 9;

    return Volume;
}

// Drivers code
int main()
{

    // space diagonal of Cube
    float d = 5;

    cout << "Volume of Cube: "
         << CubeVolume(d);

    return 0;
}

Java

// Java program to find the volume occupied
// by Cube with given space diagonal

public class GFG{

    // Function to calculate Volume
    static float CubeVolume(float d)
    {
        float Volume;

        // Formula to find Volume
        Volume = (float) (Math.sqrt(3) * Math.pow(d, 3)) / 9;

        return Volume;
    }

    // Drivers code
    public static void main(String []args)
    {

        // space diagonal of Cube
        float d = 5;

        System.out.println("Volume of Cube: " + CubeVolume(d));

    }

    // This code is contributed by Ryuga
    }

Python3

# Python 3 program to find the volume occupied
# by Cube with given space diagonal
from math import sqrt, pow

# Function to calculate Volume
def CubeVolume(d):

    # Formula to find Volume
    Volume = (sqrt(3) * pow(d, 3)) / 9

    return Volume

# Drivers code
if __name__ == '__main__':

    # space diagonal of Cube
    d = 5

    print("Volume of Cube:",'{0:.6}' .
                format(CubeVolume(d)))

# This code is contributed
# by SURENDRA_GANGWAR

C#

// C# program to find the volume occupied
// by Cube with given space diagonal
using System;

public class GFG{

    // Function to calculate Volume
    static float CubeVolume(float d)
    {
        float Volume;

        // Formula to find Volume
        Volume = (float) (Math.Sqrt(3) * Math.Pow(d, 3)) / 9;

        return Volume;
    }

    // Drivers code
    public static void Main()
    {

        // space diagonal of Cube
        float d = 5;

        Console.WriteLine("Volume of Cube: {0:F4}" , CubeVolume(d));

    }

    // This code is contributed by mits
    }

PHP

<?php
// PHP program to find the volume occupied
// by Cube with given space diagonal

// Function to calculate Volume
function CubeVolume($d)
{
    $Volume;

    // Formula to find Volume
    $Volume = (sqrt(3) * pow($d, 3)) / 9;

    return $Volume;
}

// Driver code

// space diagonal of Cube
$d = 5;

echo "Volume of Cube: ",
         CubeVolume($d);

// This code is contributed by akt_mit
?>

Javascript

<script>

// javascript program to find the volume occupied
// by Cube with given space diagonal

// Function to calculate Volume
function CubeVolume( d)
{
    let Volume;

    // Formula to find Volume
    Volume = (Math.sqrt(3) * Math.pow(d, 3)) / 9;

    return Volume;
}

// Drivers code

    // space diagonal of Cube
    let d = 5;

   document.write( "Volume of Cube: "
         + CubeVolume(d).toFixed(4));

// This code contributed by gauravrajput1

</script>

Output:

Volume of Cube: 24.0563

Time Complexity: O(1)

Auxiliary Space: O(1)