Given here is a right circular cone of radius r and perpendicular height h, which is inscribed in a cube which in turn is inscribed in a sphere, the task is to find the radius of the sphere.
Examples:
Input: h = 5, r = 6 Output: 1.57306 Input: h = 8, r = 11 Output: 2.64156
Approach:
- Let the side of the cube = a
- Let the radius of the sphere = R
- We know, a=h*r?2/(h+?2*r)(Please refer here)
- Also, R=a/2(Please refer here)
- So, R = (h*r?2/(h+?2*r))/2
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest sphere// which is inscribed within a cube which in turn// inscribed within a right circular cone#include <bits/stdc++.h>using namespace std;// Function to find the radius of the spherefloat sphereSide(float h, float r){ // height and radius cannot be negative if (h < 0 && r < 0) return -1; // radius of the sphere float R = ((h * r * sqrt(2)) / (h + sqrt(2) * r)) / 2; return R;}// Driver codeint main(){ float h = 5, r = 6; cout << sphereSide(h, r) << endl; return 0;} |
Java
// Java Program to find the biggest sphere// which is inscribed within a cube which in turn// inscribed within a right circular coneimport java.lang.Math;class GFG{ // Function to find the radius of the spherestatic float sphereSide(float h, float r){ // height and radius cannot be negative if (h < 0 && r < 0) return -1; // radius of the sphere float R = (float)((h * r * Math.sqrt(2)) / (h + Math.sqrt(2) * r)) / 2; return R;}// Driver codepublic static void main(String[] args){ float h = 5, r = 6; System.out.println(sphereSide(h, r));}}// This code is contributed by Code_Mech. |
Python3
# Program to find the biggest sphere# which is inscribed within a cube which in turn# inscribed within a right circular coneimport math# Function to find the radius of the spheredef sphereSide(h, r): # height and radius cannot be negative if h < 0 and r < 0: return -1 # radius of the sphere R = (((h * r * math.sqrt(2))) / (h + math.sqrt(2) * r) / 2) return R# Driver codeh = 5; r = 6print(sphereSide(h, r))# This code is contributed by Shrikant13 |
C#
// C# Program to find the biggest sphere// which is inscribed within a cube which in turn// inscribed within a right circular coneusing System;class GFG{ // Function to find the radius of the spherestatic float sphereSide(float h, float r){ // height and radius cannot be negative if (h < 0 && r < 0) return -1; // radius of the sphere float R = (float)((h * r * Math.Sqrt(2)) / (h + Math.Sqrt(2) * r)) / 2; return R;}// Driver codepublic static void Main(){ float h = 5, r = 6; Console.WriteLine(sphereSide(h, r));}}// This code is contributed by Code_Mech |
PHP
<?php// PHP Program to find the biggest sphere// which is inscribed within a cube which in turn// inscribed within a right circular cone// Function to find the radius of the spherefunction sphereSide($h, $r){ // height and radius cannot be negative if ($h < 0 && $r < 0) return -1; // radius of the sphere $R = (($h * $r * sqrt(2)) / ($h + sqrt(2) * $r)) / 2; return $R;}// Driver code$h = 5; $r = 6;echo(sphereSide($h, $r));// This code is contributed by Code_Mech.?> |
Javascript
<script>// javascript Program to find the biggest sphere// which is inscribed within a cube which in turn// inscribed within a right circular cone// Function to find the radius of the spherefunction sphereSide(h , r){ // height and radius cannot be negative if (h < 0 && r < 0) return -1; // radius of the sphere var R = ((h * r * Math.sqrt(2)) / (h + Math.sqrt(2) * r)) / 2; return R;}// Driver codevar h = 5, r = 6;document.write(sphereSide(h, r).toFixed(5));// This code is contributed by Amit Katiyar </script> |
Output
1.57306
Time Complexity: O(1)
Auxiliary Space: O(1)
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