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Volume of largest right circular cylinder within a Sphere
  • Last Updated : 17 Mar, 2021

Given a sphere of radius R  . The task is to find volume of the biggest right circular cylinder that can be inscribed within it.
Examples
 

Input : R = 4
Output : 77.3495


Input : R = 5
Output : 151.073

 

 

Approach
let r be the radius of the right circular cylinder, and h be it’s height.
Volume of the cylinder, V = π*r2*h
Also, r2 = R2 – h2 
or, V = π*(R2 – h2)*h 
or, dV/dh = π*(R2 – 3*h2)
Setting it to zero, we get h = R/√3 
So, Vmax = 2πR3/3√3 
Below is the implementation of the above approach: 
 

C++




// C++ Program to find the biggest right circular cylinder
// that can be fit within a sphere
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the biggest right circular cylinder
float cyl(float R)
{
 
    // radius cannot be negative
    if (R < 0)
        return -1;
 
    // volume of cylinder
    float V = (2 * 3.14 * pow(R, 3)) / (3 * sqrt(3));
    return V;
}
 
// Driver code
int main()
{
    float R = 4;
 
    cout << cyl(R) << endl;
 
    return 0;
}

Java




// Java Program to find the biggest
// right circular cylinder that can
// be fit within a sphere
import java.io.*;
 
class GFG
{
 
// Function to find the biggest
// right circular cylinder
static float cyl(float R)
{
 
    // radius cannot be negative
    if (R < 0)
        return -1;
 
    // volume of cylinder
    float V = (float)((2 * 3.14 * Math.pow(R, 3)) /
                      (3 * Math.sqrt(3)));
    return V;
}
 
// Driver code
public static void main (String[] args)
{
    float R = 4;
 
    System.out.print( cyl(R));
}
}
 
// This code is contributed by anuj_67..

Python 3




# Python 3 Program to find the biggest
# right circular cylinder that can be
# fit within a sphere
import math
 
# Function to find the biggest right
# circular cylinder
def cyl(R):
     
    # radius cannot be negative
    if (R < 0):
        return -1
 
    # volume of cylinder
    V = ((2 * 3.14 * math.pow(R, 3)) /
                (3 * math.sqrt(3)));
    return float(V)
 
# Driver code
R = 4
print(cyl(R))
 
# This code is contributed
# by PrinciRaj1992

C#




// C# Program to find the biggest
// right circular cylinder that can
// be fit within a sphere
using System;
 
class GFG
{
 
// Function to find the biggest
// right circular cylinder
static float cyl(float R)
{
 
    // radius cannot be negative
    if (R < 0)
        return -1;
 
    // volume of cylinder
    float V = (float)((2 * 3.14 * Math.Pow(R, 3)) /
                             (3 * Math.Sqrt(3)));
    return V;
}
 
// Driver code
public static void Main ()
{
    float R = 4;
 
    Console.WriteLine( cyl(R));
}
}
 
// This code is contributed by shs

PHP




<?php
// PHP Program to find the biggest right circular cylinder
// that can be fit within a sphere
 
 
 
// Function to find the biggest right circular cylinder
function cyl($R)
{
 
    // radius cannot be negative
    if ($R < 0)
        return -1;
 
    // volume of cylinder
    $V = (2 * 3.14 * pow($R, 3)) / (3 * sqrt(3));
    return $V;
}
 
// Driver code
    $R = 4;
 
    echo cyl($R);
 
// This code is contributed by shs
 
?>

Javascript




<script>
 
// javascript Program to find the biggest
// right circular cylinder that can
// be fit within a sphere
 
// Function to find the biggest
// right circular cylinder
function cyl(R)
{
 
    // radius cannot be negative
    if (R < 0)
        return -1;
 
    // volume of cylinder
    var V = ((2 * 3.14 * Math.pow(R, 3)) /
                      (3 * Math.sqrt(3)));
    return V;
}
 
// Driver code
var R = 4;
 
document.write( cyl(R).toFixed(4));
 
// This code contributed by shikhasingrajput
 
</script>
Output: 
77.3495

 

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