# Largest cone that can be inscribed within a cube

• Last Updated : 27 Jul, 2022

Given here is a cube of side length a. We have to find the height and the radius of the biggest right circular cone that can be inscribed within it.
Examples

```Input : a = 6
Output : r = 4.24264, h = 6

Input : a = 10
Output : r = 7.07107, h = 10```

Approach
Let height of the cone = h
and, radius of the cone = r.
From the diagram, we can clearly understand that,

• r = a/âˆš2
• h = a

Below is the implementation of the above approach:

## C++

 `// C++ Program to find the biggest cone``// inscribed within a cube` `#include ``using` `namespace` `std;` `// Function to find the radius of the cone``float` `coneRadius(``float` `a)``{` `    ``// side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// radius of the cone``    ``float` `r = a / ``sqrt``(2);``    ``return` `r;``}` `// Function to find the height of the cone``float` `coneHeight(``float` `a)``{``    ``// side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// height of the cone``    ``float` `h = a;``    ``return` `h;``}` `// Driver code``int` `main()``{``    ``float` `a = 6;` `    ``cout << ``"r = "` `<< coneRadius(a) << ``", "``        ``<< ``"h = "` `<< coneHeight(a) << endl;` `    ``return` `0;``}`

## Java

 `// Java Program to find the biggest``// cone inscribed within a cube``import` `java.util.*;``import` `java.lang.*;` `class` `GFG``{``// Function to find the radius``// of the cone``static` `float` `coneRadius(``float` `a)``{` `    ``// side cannot be negative``    ``if` `(a < ``0``)``        ``return` `-``1``;` `    ``// radius of the cone``    ``float` `r = (``float``)(a / Math.sqrt(``2``));``    ``return` `r;``}` `// Function to find the height``// of the cone``static` `float` `coneHeight(``float` `a)``{``    ``// side cannot be negative``    ``if` `(a < ``0``)``        ``return` `-``1``;` `    ``// height of the cone``    ``float` `h = a;``    ``return` `h;``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``float` `a = ``6``;` `    ``System.out.println(``"r = "` `+ coneRadius(a) +``                    ``", "` `+ ``"h = "` `+ coneHeight(a));``}``}` `// This code is contributed``// by Akanksha Rai`

## Python 3

 `# Python 3 Program to find the biggest``# cone inscribed within a cube``import` `math` `# Function to find the radius``# of the cone``def` `coneRadius(a):` `    ``# side cannot be negative``    ``if` `(a < ``0``):``        ``return` `-``1` `    ``# radius of the cone``    ``r ``=` `a ``/` `math.sqrt(``2``)``    ``return` `r` `# Function to find the height of the cone``def` `coneHeight(a):` `    ``# side cannot be negative``    ``if` `(a < ``0``):``        ``return` `-``1` `    ``# height of the cone``    ``h ``=` `a``    ``return` `h` `# Driver code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``a ``=` `6` `    ``print``(``"r = "``, coneRadius(a) ,``          ``"h = "``, coneHeight(a))` `# This code is contributed by ChitraNayal`

## C#

 `// C# Program to find the biggest``// cone inscribed within a cube``using` `System;` `class` `GFG``{``// Function to find the radius``// of the cone``static` `float` `coneRadius(``float` `a)``{` `    ``// side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// radius of the cone``    ``float` `r = (``float``)(a / Math.Sqrt(2));``    ``return` `r;``}` `// Function to find the height``// of the cone``static` `float` `coneHeight(``float` `a)``{``    ``// side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// height of the cone``    ``float` `h = a;``    ``return` `h;``}` `// Driver code``public` `static` `void` `Main()``{``    ``float` `a = 6;` `    ``Console.WriteLine(``"r = "` `+ coneRadius(a) +``                       ``", "` `+ ``"h = "` `+ coneHeight(a));``}``}` `// This code is contributed``// by Akanksha Rai`

## PHP

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## Javascript

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Output:

`r = 4.24264, h = 6`

Time Complexity: O(1)

Auxiliary Space: O(1)

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