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Largest right circular cylinder within a frustum

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  • Last Updated : 20 Aug, 2022
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Given a frustum of height h       , top-radius r       & base-radius R       . The task is to find the volume of biggest right circular cylinder that can be inscribed within it.
Examples: 
 

Input  : r = 5, R = 10, h = 4
Output : 314

Input : r = 7, R = 11, h = 6
Output : 923.16

 

 

Approach
Let: 
 

  • The height of the cylinder = h1
  • Radius of the cylinder = r1

From the figure it is clear that: 
 

  • Height of the cylinder = Height of frustum
  • Radius of the cylinder = Rop-radius of the frustum

So, 
 

h1 = h
r1 = r

Below is the implementation of the above approach: 
 

C++




// C++ Program to find the biggest right circular cylinder
// that can be fit within a frustum
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the biggest right circular cylinder
float cyl(float r, float R, float h)
{
    // radii and height cannot be negative
    if (h < 0 && r < 0 && R < 0)
        return -1;
 
    // radius of right circular cylinder
    float r1 = r;
    // height of right circular cylinder
    float h1 = h;
    // volume of right circular cylinder
    float V = 3.14 * pow(r1, 2) * h1;
 
    return V;
}
 
// Driver code
int main()
{
    float r = 7, R = 11, h = 6;
 
    cout << cyl(r, R, h) << endl;
 
    return 0;
}

Java




// Java Program to find the biggest right circular cylinder
// that can be fit within a frustum
 
import java.io.*;
 
class GFG {
 
 
// Function to find the biggest right circular cylinder
 static float cyl(float r, float R, float h)
{
    // radii and height cannot be negative
    if (h < 0 && r < 0 && R < 0)
        return -1;
 
    // radius of right circular cylinder
    float r1 = r;
    // height of right circular cylinder
    float h1 = h;
    // volume of right circular cylinder
    float V = (float)(3.14 * Math.pow(r1, 2) * h1);
 
    return V;
}
 
// Driver code
    public static void main (String[] args) {
            float r = 7, R = 11, h = 6;
 
    System.out.print( cyl(r, R, h));
    }
}
// This code is contributed by anuj_67..

Python3




# Python3 Program to find the biggest right circular cylinder
# that can be fit within a frustum
 
# Function to find the biggest right circular cylinder
def cyl(r, R, h) :
 
    # radii and height cannot be negative
    if (h < 0 and r < 0 and R < 0) :
        return -1
 
    # radius of right circular cylinder
    r1 = r
    # height of right circular cylinder
    h1 = h
    # volume of right circular cylinder
    V = 3.14 * pow(r1, 2) * h1
 
    return round(V,2)
 
 
# Driver code
if __name__ == "__main__" :
 
    r, R, h = 7, 11, 6
 
    print(cyl(r, R, h))
 
# This code is contributed by Ryuga

C#




// C# Program to find the biggest right circular cylinder
// that can be fit within a frustum
using System;
 
class GFG {
 
 
// Function to find the biggest right circular cylinder
static float cyl(float r, float R, float h)
{
    // radii and height cannot be negative
    if (h < 0 && r < 0 && R < 0)
        return -1;
 
    // radius of right circular cylinder
    float r1 = r;
    // height of right circular cylinder
    float h1 = h;
    // volume of right circular cylinder
    float V = (float)(3.14 * Math.Pow(r1, 2) * h1);
 
    return V;
}
 
// Driver code
    public static void Main () {
            float r = 7, R = 11, h = 6;
 
    Console.WriteLine( cyl(r, R, h));
    }
}
// This code is contributed by anuj_67..

PHP




<?php
// PHP Program to find the biggest
// right circular cylinder that can
// be fit within a frustum
 
// Function to find the biggest
// right circular cylinder
function cyl($r, $R, $h)
{
    // radii and height cannot be negative
    if ($h < 0 && $r < 0 && $R < 0)
        return -1;
 
    // radius of right circular cylinder
    $r1 = $r;
     
    // height of right circular cylinder
    $h1 = $h;
     
    // volume of right circular cylinder
    $V = (3.14 * pow($r1, 2) * $h1);
 
    return $V;
}
 
// Driver code
$r = 7; $R = 11; $h = 6;
 
echo cyl($r, $R, $h);
     
// This code is contributed
// by Mukul Singh.

Javascript




<script>
// javascript Program to find the biggest right circular cylinder
// that can be fit within a frustum
 
// Function to find the biggest right circular cylinder
 function cyl(r , R , h)
{
 
    // radii and height cannot be negative
    if (h < 0 && r < 0 && R < 0)
        return -1;
 
    // radius of right circular cylinder
    var r1 = r;
     
    // height of right circular cylinder
    var h1 = h;
     
    // volume of right circular cylinder
    var V = (3.14 * Math.pow(r1, 2) * h1);
    return V;
}
 
// Driver code
var r = 7, R = 11, h = 6;
document.write( cyl(r, R, h).toFixed(5));
 
// This code is contributed by Princi Singh
</script>

Output: 

923.16

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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