# Largest cube that can be inscribed within the sphere

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 = 8Output:9.2376Input:r = 5Output: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 = 2ror,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 cube ` `float` `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 code ` `int` `main() ` `{ ` ` ` `float` `r = 5; ` ` ` `cout << largestCube(r) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## 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 ` |

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## Python3

`# Python 3 Program to find the biggest ` `# cube inscribed within a sphere ` `from` `math ` `import` `sqrt ` ` ` `# Function to find the side of the cube ` `def` `largestCube(r): ` ` ` ` ` `# radius cannot be negative ` ` ` `if` `(r < ` `0` `): ` ` ` `return` `-` `1` ` ` ` ` `# side of the cube ` ` ` `a ` `=` `(` `2` `*` `r) ` `/` `sqrt(` `3` `) ` ` ` `return` `a ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` `r ` `=` `5` ` ` `print` `(` `"{0:.6}"` `.` `format` `(largestCube(r))) ` ` ` `# This code is contributed ` `# by SURENDRA_GANGWAR ` |

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## 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 ` |

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## 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 ` `?> ` |

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**Output:**

5.7735

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