# 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 = aâˆš2**, 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 = 2aâˆš2/3** and height of cylinder with respect to cube, **h = 2a/3**.

So, volume of the cylinder, **V = 16Ï€a^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;` `}` |

## 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.` |

## 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` |

## 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` |

## 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` `?>` |

## Javascript

`<script>` `// javascript 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` ` ` `var` `r = (2 * a *(Math.sqrt (2)) / 3);` ` ` `// height of right circular cylinder` ` ` `var` `h = (2 * a) / 3;` ` ` `// volume of right circular cylinder` ` ` `var` `V =(3.14 *(Math.pow(r, 2) * h));` ` ` `return` `V;` `}` `// Driver code` `var` `a = 5;` `document.write(cyl(a).toFixed(5));` `// This code contributed by Princi Singh` `</script>` |

**Output:**

232.593

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)