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

Given a cube of side length **a**, which inscribes a sphere which in turn inscribes a right circular cone. The task is to find the largest possible volume of this cone.

**Examples:**

Input:a = 5Output:58.1481Input:a = 8Output:238.175

**Approach**:

Let, the height of right circular cone = **h**.

Radius of the cone = **r**

Radius of the sphere = **R**

We, know radius of the sphere inside the cube, **r = a/2**. Please refer ( Largest sphere that can be inscribed inside a cube).

Also, height of cone inside the sphere, **h = 4r/3**.

radius of cone inside the sphere, **r = 2√2r/3**. Please refer (Largest right circular cone that can be inscribed within a sphere).

So, height of the cone inside the sphere which in turn is inscribed within a cube, **h = 2a/3**.

Radius of the cone inside the sphere which in turn is inscribed within a cube, **r = √2a/3**.

Below is the implementation of the above approach:

## C++

`// C++ Program to find the biggest right circular cone ` `// that can be inscribed within a right circular cone ` `// which in turn is inscribed within a cube ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the biggest right circular cone ` `float` `cone(` `float` `a) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(a < 0) ` ` ` `return` `-1; ` ` ` ` ` `// radius of right circular cone ` ` ` `float` `r = (a * ` `sqrt` `(2)) / 3; ` ` ` ` ` `// height of right circular cone ` ` ` `float` `h = (2 * a) / 3; ` ` ` ` ` `// volume of right circular cone ` ` ` `float` `V = 3.14 * ` `pow` `(r, 2) * h; ` ` ` ` ` `return` `V; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `a = 5; ` ` ` `cout << cone(a) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find the biggest right circular cone ` `// that can be inscribed within a right circular cone ` `// which in turn is inscribed within a cube ` `import` `java.io.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the biggest right circular cone ` `static` `float` `cone(` `float` `a) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(a < ` `0` `) ` ` ` `return` `-` `1` `; ` ` ` ` ` `// radius of right circular cone ` ` ` `float` `r = (` `float` `) (a * Math.sqrt(` `2` `)) / ` `3` `; ` ` ` ` ` `// height of right circular cone ` ` ` `float` `h = (` `2` `* a) / ` `3` `; ` ` ` ` ` `// volume of right circular cone ` ` ` `float` `V = (` `float` `)(` `3.14` `*Math. pow(r, ` `2` `) * h); ` ` ` ` ` `return` `V; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main (String[] args) ` `{ ` ` ` `float` `a = ` `5` `; ` ` ` `System.out.println( cone(a)); ` `} ` `} ` ` ` `// This code is contributed by anuj_67.. ` |

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## Python3

`# Python3 Program to find the biggest right ` `# circular cone that can be inscribed within ` `# a right circular cone which in turn is ` `# inscribed within a cube ` `import` `math ` ` ` `# Function to find the biggest ` `# right circular cone ` `def` `cone(a): ` ` ` ` ` `# side cannot be negative ` ` ` `if` `(a < ` `0` `): ` ` ` `return` `-` `1` `; ` ` ` ` ` `# radius of right circular cone ` ` ` `r ` `=` `(a ` `*` `math.sqrt(` `2` `)) ` `/` `3` `; ` ` ` ` ` `# height of right circular cone ` ` ` `h ` `=` `(` `2` `*` `a) ` `/` `3` `; ` ` ` ` ` `# volume of right circular cone ` ` ` `V ` `=` `3.14` `*` `math.` `pow` `(r, ` `2` `) ` `*` `h; ` ` ` ` ` `return` `V; ` ` ` `# Driver code ` `a ` `=` `5` `; ` `print` `(cone(a)); ` ` ` `# This code is contributed by ` `# Shivi_Aggarwal ` |

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## C#

`// C# Program to find the biggest ` `// right circular cone that can be ` `// inscribed within a right circular cone ` `// which in turn is inscribed within a cube ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the biggest ` `// right circular cone ` `static` `double` `cone(` `double` `a) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(a < 0) ` ` ` `return` `-1; ` ` ` ` ` `// radius of right circular cone ` ` ` `double` `r = (` `double` `) (a * Math.Sqrt(2)) / 3; ` ` ` ` ` `// height of right circular cone ` ` ` `double` `h = (2 * a) / 3; ` ` ` ` ` `// volume of right circular cone ` ` ` `double` `V = (` `double` `)(3.14 * Math.Pow(r, 2) * h); ` ` ` ` ` `return` `Math.Round(V,4); ` `} ` ` ` `// Driver code ` `static` `void` `Main () ` `{ ` ` ` `double` `a = 5; ` ` ` `Console.WriteLine(cone(a)); ` `} ` `} ` ` ` `// This code is contributed by chandan_jnu ` |

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## PHP

`<?php ` `// PHP Program to find the biggest right ` `// circular cone that can be inscribed ` `// within a right circular cone which in ` `// turn is inscribed within a cube ` ` ` `// Function to find the biggest ` `// right circular cone ` `function` `cone(` `$a` `) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(` `$a` `< 0) ` ` ` `return` `-1; ` ` ` ` ` `// radius of right circular cone ` ` ` `$r` `= (` `$a` `* sqrt(2)) / 3; ` ` ` ` ` `// height of right circular cone ` ` ` `$h` `= (2 * ` `$a` `) / 3; ` ` ` ` ` `// volume of right circular cone ` ` ` `$V` `= 3.14 * pow(` `$r` `, 2) * ` `$h` `; ` ` ` ` ` `return` `$V` `; ` `} ` ` ` `// Driver code ` `$a` `= 5; ` `echo` `round` `(cone(` `$a` `), 4); ` ` ` `// This code is contributed by Ryuga ` `?> ` |

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**Output:**

58.1481

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