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; ` `} ` |

*chevron_right*

*filter_none*

## PHP

**Output:**

232.593

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