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Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone

  • Last Updated : 18 Mar, 2021

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
 



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 sphere
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 = ((h * r * sqrt(2)) / (h + sqrt(2) * r)) / 2;
 
    return R;
}
 
// Driver code
int 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 cone
import java.lang.Math;
 
class GFG
{
     
// Function to find the radius of the sphere
static 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 code
public 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 cone
import math
 
# Function to find the radius of the sphere
def 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 code
h = 5; r = 6
print(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 cone
using System;
 
class GFG
{
     
// Function to find the radius of the sphere
static 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 code
public 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 sphere
function 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 sphere
function 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 code
var h = 5, r = 6;
 
document.write(sphereSide(h, r).toFixed(5));
 
 
// This code is contributed by Amit Katiyar
 
</script>
Output: 
1.57306

 

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