# 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 = 5Output:Volume of Cube: 24.0563Input:d = 10Output: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)

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