Largest sphere that can be inscribed inside a cube

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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 

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PHP

Output:

2.5


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