Given a right circular cone of radius r and perpendicular height h. We have to find the side length of the biggest cube that can be inscribed within it.
Examples:
Input : h = 5, r = 6 Output : 3.14613 Input : h = 8, r = 12 Output : 5.43698
Approach:
Let, side of the cube = a.
From the diagram, we can clearly understand using the properties of triangles: BC/AB = DE/AD.
Therefore,
r/h = (a/?2)/(h-a) or, a = h*r?2/(h+?2*r)
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest cube// inscribed within a right circular cone#include <bits/stdc++.h>using namespace std;// Function to find the side of the cubefloat cubeSide(float h, float r){ // height and radius cannot be negative if (h < 0 && r < 0) return -1; // side of the cube float a = (h * r * sqrt(2)) / (h + sqrt(2) * r); return a;}// Driver codeint main(){ float h = 5, r = 6; cout << cubeSide(h, r) << endl; return 0;} |
Java
// Java Program to find the biggest cube // which can be inscribed within a right circular coneimport java.io.*; class GFG { // Function to find the side of the cubestatic float cube(float h, float r) { // height and radius cannot be negative if (h < 0 && r < 0) return -1; // side of the cube float a = (h * r * (float)Math.sqrt(2)) / (h + (float)Math.sqrt(2) * r); return a; } // Driver code public static void main (String[] args) { float h = 5, r = 6; System.out.println( cube(h, r)); } } // this article is contributed by Ishwar Gupta |
Python 3
# Python3 Program to find the biggest cube# inscribed within a right circular coneimport math# Function to find the side of the cubedef cubeSide(h, r): # height and radius cannot # be negative if (h < 0 and r < 0): return -1 # side of the cube a = ((h * r * math.sqrt(2)) / (h + math.sqrt(2) * r)) return a# Driver codeh = 5; r = 6;print(cubeSide(h, r), "\n")# This code is contributed # by Akanksha Rai |
C#
// C# Program to find the // biggest cube which can be // inscribed within a right // circular coneusing System;class GFG { // Function to find the side // of the cubestatic float cube(float h, float r) { // height and radius cannot be negative if (h < 0 && r < 0) return -1; // side of the cube float a = (h * r * (float)Math.Sqrt(2)) / (h + (float)Math.Sqrt(2) * r); return a; } // Driver code public static void Main () { float h = 5, r = 6; Console.Write( cube(h, r)); } }// This code is contributed // by 29AjayKumar |
PHP
<?php// PHP Program to find the biggest cube// inscribed within a right circular cone// Function to find the side of the cubefunction cubeSide($h, $r){ // height and radius cannot // be negative if ($h < 0 && $r < 0) return -1; // side of the cube $a = ($h * $r * sqrt(2)) / ($h + sqrt(2) * $r); return $a;}// Driver code$h = 5;$r = 6;echo cubeSide($h, $r); // This code is contributed// by Shivi_Aggarwal?> |
Javascript
<script>// javascript Program to find the biggest cube // which can be inscribed within a right circular cone// Function to find the side of the cubefunction cube(h , r) { // height and radius cannot be negative if (h < 0 && r < 0) return -1; // side of the cube var a = (h * r * Math.sqrt(2)) / (h + Math.sqrt(2) * r); return a; } // Driver code var h = 5, r = 6;document.write( cube(h, r).toFixed(5)); // This code is contributed by 29AjayKumar </script> |
Output:
3.14613
Time Complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.
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