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Largest right circular cylinder within a cube
  • Last Updated : 18 Dec, 2018

Given a cube of side length a. The task is to find the volume of biggest right circular cylinder that can be inscribed within it.

Examples:

Input :  a = 4
Output : 50.24

Input : a = 5
Output : 98.125

Approach:
Let:

  • The height of the cylinder is h.
  • Radius of the cylinder be r.

From the diagram it is clear that:



  • The height of the cylinder = side of cube
  • Radius of the cylinder = side of the cube/2

So,

h = a
r = a/2

Below is the implementation of the above approach:

C++




// C++ Program to find the biggest right
// circular cylinder that can be fit within a cube
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the biggest right circular cylinder
float findVolume(float a)
{
    // side cannot be negative
    if (a < 0)
        return -1;
  
    // radius of right circular cylinder
    float r = a / 2;
  
    // height of right circular cylinder
    float h = a;
  
    // volume of right circular cylinder
    float V = 3.14 * pow(r, 2) * h;
  
    return V;
}
  
// Driver code
int main()
{
    float a = 5;
  
    cout << findVolume(a) << endl;
  
    return 0;
}


Java




// Java Program to find the biggest right
// circular cylinder that can be fit within a cube
  
import java.io.*;
  
class GFG {
    
  
// Function to find the biggest right circular cylinder
 static float findVolume(float a)
{
    // side cannot be negative
    if (a < 0)
        return -1;
  
    // radius of right circular cylinder
    float r = a / 2;
  
    // height of right circular cylinder
    float h = a;
  
    // volume of right circular cylinder
    float V = (float)(3.14 * Math.pow(r, 2) * h);
  
    return V;
}
  
// Driver code
  
  
    public static void main (String[] args) {
            float a = 5;
  
    System.out.print(findVolume(a));
    }
}
// This code is contributed by anuj_67..


Python3




# Python3 Program to find the biggest 
# right circular cylinder that can be 
# fit within a cube 
  
# Function to find the biggest right
# circular cylinder 
def findVolume(a) :
  
    # side cannot be negative 
    if (a < 0) : 
        return -1
  
    # radius of right circular cylinder 
    r = a / 2
  
    # height of right circular cylinder 
    h = a
  
    # volume of right circular cylinder 
    V = 3.14 * pow(r, 2) *
  
    return
  
# Driver code 
if __name__ == "__main__"
  
    a = 5
  
    print(findVolume(a))
  
# This code is contributed by Ryuga


C#




// C# Program to find the biggest right
// circular cylinder that can be fit within a cube
  
using System;
class GFG {
  
  
// Function to find the biggest right circular cylinder
static float findVolume(float a)
{
    // side cannot be negative
    if (a < 0)
        return -1;
  
    // radius of right circular cylinder
    float r = a / 2;
  
    // height of right circular cylinder
    float h = a;
  
    // volume of right circular cylinder
    float V = (float)(3.14 * Math.Pow(r, 2) * h);
  
    return V;
}
  
// Driver code
  
  
    public static void Main () {
            float a = 5;
  
   Console.WriteLine(findVolume(a));
    }
}
// This code is contributed by anuj_67..


PHP




<?php
// PHP Program to find the biggest 
// right circular cylinder that can 
// be fit within a cube
  
// Function to find the biggest
// right circular cylinder
function findVolume($a)
{
    // side cannot be negative
    if ($a < 0)
        return -1;
  
    // radius of right circular cylinder
    $r = $a / 2;
  
    // height of right circular cylinder
    $h = $a;
  
    // volume of right circular cylinder
    $V = 3.14 * pow($r, 2) * $h;
  
    return $V;
}
  
// Driver code
$a = 5;
  
echo findVolume($a) . "\n";
  
// This code is contributed 
// by Akanksha Rai


Output:

98.125

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