Given here is a sphere of radius r, the task is to find the side of the largest cube that can fit inside in it.
Examples:
Input: r = 8 Output: 9.2376 Input: r = 5 Output: 5.7735
Approach:
Side of the cube = a
Radius of the sphere = r
From the diagonal, it is clear that, diagonal of the cube = diameter of the sphere,
a?3 = 2r or, a = 2r/?3
Below is the implementation:
C++
// C++ Program to find the biggest cube// inscribed within a sphere#include <bits/stdc++.h>using namespace std;// Function to find the side of the cubefloat largestCube(float r){ // radius cannot be negative if (r < 0) return -1; // side of the cube float a = (2 * r) / sqrt(3); return a;}// Driver codeint main(){ float r = 5; cout << largestCube(r) << endl; return 0;} |
Java
// Java Program to find the biggest cube // inscribed within a sphere import java.util.*;class Solution{// Function to find the side of the cube static float largestCube(float r) { // radius cannot be negative if (r < 0) return -1; // side of the cube float a = (2 * r) / (float)Math.sqrt(3); return a; } // Driver code public static void main(String args[]){ float r = 5; System.out.println( largestCube(r)); } }//contributed by Arnab Kundu |
Python3
# Python 3 Program to find the biggest # cube inscribed within a spherefrom math import sqrt# Function to find the side of the cubedef largestCube(r): # radius cannot be negative if (r < 0): return -1 # side of the cube a = (2 * r) / sqrt(3) return a# Driver codeif __name__ == '__main__': r = 5 print("{0:.6}".format(largestCube(r)))# This code is contributed# by SURENDRA_GANGWAR |
C#
// C# Program to find the biggest cube // inscribed within a sphere using System;class Solution{// Function to find the side of the cube static float largestCube(float r) { // radius cannot be negative if (r < 0) return -1; // side of the cube float a = (2 * r) / (float)Math.Sqrt(3); return a; } // Driver code static void Main(){ float r = 5; Console.WriteLine( largestCube(r)); } }//This code is contributed by mits |
PHP
<?php// PHP Program to find the biggest // cube inscribed within a sphere // Function to find the side // of the cube function largestCube($r) { // radius cannot be negative if ($r < 0) return -1; // side of the cube $a = (float)((2 * $r) / sqrt(3)); return $a; } // Driver code $r = 5; echo largestCube($r); // This code is contributed by akt_mit?> |
Javascript
<script>// javascript Program to find the biggest cube // inscribed within a sphere // Function to find the side of the cube function largestCube(r) { // radius cannot be negative if (r < 0) return -1; // side of the cube var a = (2 * r) / Math.sqrt(3); return a; } // Driver code var r = 5; document.write( largestCube(r).toFixed(5)); // This code is contributed by 29AjayKumar </script> |
Output:
5.7735
Time Complexity: O(1)
Auxiliary Space: O(1)
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