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Largest sphere that can be inscribed inside a cube
  • Last Updated : 17 Mar, 2021
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Given here is a cube of side length a, the task is to find the biggest sphere that can be inscribed within it.
Examples: 
 

Input: a = 4
Output: 2

Input: a = 5
Output: 2.5

 

Approach
 

From the 2d diagram it is clear that, 2r = a
where, a = side of the cube 
r = radius of the sphere 
so r = a/2.



Below is the implementation of the above approach:
 

C++




// C++ Program to find the biggest sphere
// inscribed within a cube
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the radius of the sphere
float sphere(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of the sphere
    float r = a / 2;
 
    return r;
}
 
// Driver code
int main()
{
    float a = 5;
    cout << sphere(a) << endl;
 
    return 0;
}

Java




// Java Program to find the biggest sphere
// inscribed within a cube
 
class GFG{
// Function to find the radius of the sphere
static float sphere(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of the sphere
    float r = a / 2;
 
    return r;
}
 
// Driver code
public static void main(String[] args)
{
    float a = 5;
    System.out.println(sphere(a));
 
}
}
// This code is contributed by mits

Python3




# Python 3 Program to find the biggest
# sphere inscribed within a cube
 
# Function to find the radius
# of the sphere
def sphere(a):
     
    # side cannot be negative
    if (a < 0):
        return -1
 
    # radius of the sphere
    r = a / 2
 
    return r
 
# Driver code
if __name__ == '__main__':
    a = 5
    print(sphere(a))
 
# This code is contributed
# by SURENDRA_GANGWAR

C#




// C# Program to find the biggest
// sphere inscribed within a cube
using System;
 
class GFG
{
// Function to find the radius
// of the sphere
static float sphere(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of the sphere
    float r = a / 2;
 
    return r;
}
 
// Driver code
static public void Main ()
{
    float a = 5;
    Console.WriteLine(sphere(a));
}
}
 
// This code is contributed by ajit

PHP




<?php
// PHP Program to find the biggest
// sphere inscribed within a cube
 
// Function to find the radius
// of the sphere
function sphere($a)
{
 
    // side cannot be negative
    if ($a < 0)
        return -1;
 
    // radius of the sphere
    $r = ($a / 2);
 
    return $r;
}
 
// Driver code
$a = 5;
echo sphere($a);
 
// This code is contributed by akt_mit
?>

Javascript




<script>
// javascript Program to find the biggest sphere
// inscribed within a cube
 
// Function to find the radius of the sphere
function sphere(a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of the sphere
    var r = a / 2;
    return r;
}
 
// Driver code
var a = 5;
document.write(sphere(a));
 
// This code is contributed by 29AjayKumar
</script>
Output: 
2.5

 

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