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

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

**Examples:**

Input:a = 5Output:232.593Input:a = 8Output:952.699

**Approach**:

From the figure, it is very clear, height of cone, **H = a** and radius of the cone, **R = a√2**, please refer Largest cone that can be inscribed within a cube.

and, radius of the cylinder, **r = 2R/3** and height of the cylinder, **h = 2H/3**, please refer Largest right circular cylinder that can be inscribed within a cone.

So, radius of cylinder with respect to cube, **r = 2a√2/3** and height of cylinder with respect to cube, **h = 2a/3**.

So, volume of the cylinder, **V = 16πa^3/27**.

Below is the implementation of the above approach:

## C++

`// C++ Program to find the biggest right circular ` `// cylinder 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 cylinder ` `float` `cyl(` `float` `a) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(a < 0) ` ` ` `return` `-1; ` ` ` ` ` `// radius of right circular cylinder ` ` ` `float` `r = (2 * a * ` `sqrt` `(2)) / 3; ` ` ` ` ` `// height of right circular cylinder ` ` ` `float` `h = (2 * a) / 3; ` ` ` ` ` `// volume of right circular cylinder ` ` ` `float` `V = 3.14 * ` `pow` `(r, 2) * h; ` ` ` ` ` `return` `V; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `a = 5; ` ` ` `cout << cyl(a) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find the biggest right circular ` `// cylinder that can be inscribed within a right ` `// circular cone which in turn is inscribed ` `// within a cube ` `import` `java.lang.Math; ` ` ` `class` `cfg ` `{ ` ` ` `// Function to find the biggest ` `// right circular cylinder ` `static` `float` `cyl(` `float` `a) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(a < ` `0` `) ` ` ` `return` `-` `1` `; ` ` ` ` ` `// radius of right circular cylinder ` ` ` `float` `r = (` `2` `* a *(` `float` `)(Math.sqrt (` `2` `)) / ` `3` `); ` ` ` ` ` `// height of right circular cylinder ` ` ` `float` `h = (` `2` `* a) / ` `3` `; ` ` ` ` ` `// volume of right circular cylinder ` ` ` `float` `V =(` `3` `.14f *(` `float` `)(Math.pow(r, ` `2` `) * h)); ` ` ` ` ` `return` `V; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `float` `a = ` `5` `; ` ` ` `System.out.println(cyl(a)); ` `} ` `} ` ` ` `// This code is contributed by Mukul Singh. ` |

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## Python3

`# Python3 Program to find the biggest ` `# right circular cylinder that can be ` `# inscribed within a right circular ` `# cone which in turn is inscribed ` `# within a cube ` `import` `math as mt ` ` ` `# Function to find the biggest ` `# right circular cylinder ` `def` `cyl(a): ` ` ` ` ` `# side cannot be negative ` ` ` `if` `(a < ` `0` `): ` ` ` `return` `-` `1` ` ` ` ` `# radius of right circular cylinder ` ` ` `r ` `=` `(` `2` `*` `a ` `*` `mt.sqrt(` `2` `)) ` `/` `3` ` ` ` ` `# height of right circular cylinder ` ` ` `h ` `=` `(` `2` `*` `a) ` `/` `3` ` ` ` ` `# volume of right circular cylinder ` ` ` `V ` `=` `3.14` `*` `pow` `(r, ` `2` `) ` `*` `h ` ` ` ` ` `return` `V ` ` ` `# Driver code ` `a ` `=` `5` `print` `(cyl(a)) ` ` ` `# This code is contributed by ` `# Mohit kumar 29 ` |

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## C#

`// C# Program to find the biggest ` `// right circular cylinder 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 cylinder ` ` ` `static` `float` `cyl(` `float` `a) ` ` ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(a < 0) ` ` ` `return` `-1; ` ` ` ` ` `// radius of right circular cylinder ` ` ` `float` `r = (2 * a * (` `float` `)(Math.Sqrt (2)) / 3); ` ` ` ` ` `// height of right circular cylinder ` ` ` `float` `h = (2 * a) / 3; ` ` ` ` ` `// volume of right circular cylinder ` ` ` `float` `V =(3.14f * (` `float` `)(Math.Pow(r, 2) * h)); ` ` ` `return` `V; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `float` `a = 5; ` ` ` `Console.Write(cyl(a)); ` ` ` `} ` `} ` ` ` `// This code is contributed by Rajput-Ji ` |

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## PHP

`<?php ` `// PHP Program to find the biggest right ` `// circular cylinder that can be inscribed ` `// within a right circular cone which in ` `// turn is inscribed within a cube ` ` ` `// Function to find the biggest ` `// right circular cylinder ` `function` `cyl( ` `$a` `) ` `{ ` ` ` ` ` `// side cannot be negative ` ` ` `if` `(` `$a` `< 0) ` ` ` `return` `-1; ` ` ` ` ` `// radius of right circular cylinder ` ` ` `$r` `= (2 * ` `$a` `* sqrt(2)) / 3; ` ` ` ` ` `// height of right circular cylinder ` ` ` `$h` `= (2 * ` `$a` `) / 3; ` ` ` ` ` `// volume of right circular cylinder ` ` ` `$V` `= 3.14 * pow(` `$r` `, 2) * ` `$h` `; ` ` ` ` ` `return` `$V` `; ` `} ` ` ` `// Driver code ` `$a` `= 5; ` `echo` `cyl(` `$a` `); ` ` ` `// This code is contributed by Mahadev99 ` `?> ` |

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**Output:**

232.593

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