Largest right circular cylinder within a frustum

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++

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// 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;
}

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Java

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// 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..

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Python3

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# 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

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C#

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// 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..

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PHP

Output:

923.16


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