# Largest cone that can be inscribed within a cube

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
``` ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:
Let height of the cone = h.
and, radius of the cone = r.

From the diagram, we can clearly understand that,

• r = a/√2
• 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

 ` `

Output:

```r = 4.24264, h = 6
```

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