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++ 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 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
}
|
# 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# 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 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 ?> |
<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)