# 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


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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.
Pythagorus #1 in triangle ACD:

Pythagorus #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  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

 

Output:

Volume of Cube: 24.0563


Time Complexity: O(1)

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