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

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
``` ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

Output:

```1.57306
```

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Improved By : shrikanth13, Code_Mech