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 Volumefloat CubeVolume(float d){ float Volume; // Formula to find Volume Volume = (sqrt(3) * pow(d, 3)) / 9; return Volume;}// Drivers codeint 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 diagonalfrom math import sqrt, pow# Function to calculate Volumedef CubeVolume(d): # Formula to find Volume Volume = (sqrt(3) * pow(d, 3)) / 9 return Volume# Drivers codeif __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 Volumefunction 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 Volumefunction 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)
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