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

Given a right circular cone of radius **r** and perpendicular height **h**. We have to find the side length of the biggest cube that can be inscribed within it.

**Examples**:

Input: h = 5, r = 6Output: 3.14613Input: h = 8, r = 12Output: 5.43698

**Approach**:

Let, side of the cube = **a**.

From the diagram, we can clearly understand using the properties of triangles: **BC/AB = DE/AD.**

Therefore,

r/h = (a/√2)/(h-a)or,a = h*r√2/(h+√2*r)

Below is the implementation of the above approach:

## C++

`// C++ Program to find the biggest cube ` `// inscribed within a right circular cone ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the side of the cube ` `float` `cubeSide(` `float` `h, ` `float` `r) ` `{ ` ` ` `// height and radius cannot be negative ` ` ` `if` `(h < 0 && r < 0) ` ` ` `return` `-1; ` ` ` ` ` `// side of the cube ` ` ` `float` `a = (h * r * ` `sqrt` `(2)) / (h + ` `sqrt` `(2) * r); ` ` ` ` ` `return` `a; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `h = 5, r = 6; ` ` ` ` ` `cout << cubeSide(h, r) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find the the biggest cube ` `// which can be inscribed within a right circular cone ` ` ` `import` `java.io.*; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find the side of the cube ` ` ` `static` `float` `cube(` `float` `h, ` `float` `r) ` `{ ` ` ` ` ` `// hegiht and radius cannot be negative ` ` ` `if` `(h < ` `0` `&& r < ` `0` `) ` ` ` `return` `-` `1` `; ` ` ` ` ` `// side of the cube ` ` ` `float` `a = (h * r * (` `float` `)Math.sqrt(` `2` `)) / (h + (` `float` `)Math.sqrt(` `2` `) * r); ` ` ` ` ` `return` `a; ` `} ` ` ` `// Driver code ` ` ` ` ` `public` `static` `void` `main (String[] args) { ` ` ` `float` `h = ` `5` `, r = ` `6` `; ` ` ` `System.out.println( cube(h, r)); ` ` ` `} ` `} ` ` ` `// this article is contributed by Ishwar Gupta ` |

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## Python 3

# Python3 Program to find the biggest cube

# inscribed within a right circular cone

import math

# Function to find the side of the cube

def cubeSide(h, r):

# height and radius cannot

# be negative

if (h < 0 and r < 0):
return -1
# side of the cube
a = ((h * r * math.sqrt(2)) /
(h + math.sqrt(2) * r))
return a
# Driver code
h = 5; r = 6;
print(cubeSide(h, r), "\n")
# This code is contributed
# by Akanksha Rai
[tabby title="C#"]

`// C# Program to find the the ` `// biggest cube which can be ` `// inscribed within a right ` `// circular cone ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the side ` `// of the cube ` `static` `float` `cube(` `float` `h, ` `float` `r) ` `{ ` ` ` `// hegiht and radius cannot be negative ` `if` `(h < 0 && r < 0) ` ` ` `return` `-1; ` ` ` `// side of the cube ` `float` `a = (h * r * (` `float` `)Math.Sqrt(2)) / ` ` ` `(h + (` `float` `)Math.Sqrt(2) * r); ` ` ` ` ` `return` `a; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main () ` `{ ` ` ` `float` `h = 5, r = 6; ` ` ` `Console.Write( cube(h, r)); ` `} ` `} ` ` ` `// This code is contributed ` `// by 29AjayKumar ` |

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## PHP

`<?php ` `// PHP Program to find the biggest cube ` `// inscribed within a right circular cone ` ` ` `// Function to find the side of the cube ` `function` `cubeSide(` `$h` `, ` `$r` `) ` `{ ` ` ` `// height and radius cannot ` ` ` `// be negative ` ` ` `if` `(` `$h` `< 0 && ` `$r` `< 0) ` ` ` `return` `-1; ` ` ` ` ` `// side of the cube ` ` ` `$a` `= (` `$h` `* ` `$r` `* sqrt(2)) / ` ` ` `(` `$h` `+ sqrt(2) * ` `$r` `); ` ` ` ` ` `return` `$a` `; ` `} ` ` ` `// Driver code ` `$h` `= 5; ` `$r` `= 6; ` ` ` `echo` `cubeSide(` `$h` `, ` `$r` `); ` ` ` `// This code is contributed ` `// by Shivi_Aggarwal ` `?> ` |

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**Output:**

3.14613

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