可以内接在截锥体中的直圆柱体中的最大球体

这里给出的是一个高度为h 、顶半径为r和底半径为R的截锥体，它内接一个直圆柱体，该圆柱体又内接一个球体。任务是找到这个球体的最大可能体积。
例子：

Input: r = 5, R = 8, h = 11
Output: 523.333

Input: r = 9, R = 14, h = 20
Output:3052.08

方法：让圆柱体的高度 = H ，球体的半径 = x
我们知道，截锥体内接圆柱体的高度和半径分别等于截头体的高度和顶部半径（请参考这里）。所以圆柱体的高度= h ，圆柱体的半径= r 。
此外，内接圆柱体的球体半径等于圆柱体的半径（请参阅此处），因此x = r 。
因此，球体的体积V = 4*π*r^3/3 。
下面是上述方法的实现：

C++

// C++ Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is inscribed
// within a frustum
#include 
using namespace std;
 
// Function to find the biggest sphere
float sph(float r, float R, float h)
{
 
    // the radii and height cannot be negative
    if (r < 0 && R < 0 && h < 0)
        return -1;
 
    // radius of the sphere
    float x = r;
 
    // volume of the sphere
    float V = (4 * 3.14 * pow(r, 3)) / 3;
 
    return V;
}
 
// Driver code
int main()
{
    float r = 5, R = 8, h = 11;
    cout << sph(r, R, h) << endl;
 
    return 0;
}

Java

// Java Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is inscribed
// within a frustum
import java.lang.Math;
 
class gfg
{
     
// Function to find the biggest sphere
static float sph(float r, float R, float h)
{
 
    // the radii and height cannot be negative
    if (r < 0 && R < 0 && h < 0)
        return -1;
 
    // radius of the sphere
    float x = r;
 
    // volume of the sphere
    float V = (float)(4 * 3.14f * Math.pow(r, 3)) / 3;
 
    return V;
}
 
// Driver code
public static void main(String[] args)
{
    float r = 5, R = 8, h = 11;
    System.out.println(sph(r, R, h));
}
}
 
// This Code is contributed by Code_Mech.

Python3

# Python3 Program to find the biggest sphere
# that can be inscribed within a right
# circular cylinder which in turn is inscribed
# within a frustum
import math as mt
 
# Function to find the biggest sphere
def sph(r, R, h):
 
    # the radii and height cannot
    # be negative
    if (r < 0 and R < 0 and h < 0):
        return -1
 
    # radius of the sphere
    x = r
 
    # volume of the sphere
    V = (4 * 3.14 * pow(r, 3)) / 3
 
    return V
 
# Driver code
r, R, h = 5, 8, 11
print(sph(r, R, h))
 
# This code is contributed by
# Mohit kumar 29

C#

// C# Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is
// inscribed within a frustum
using System;
 
class gfg
{
     
    // Function to find the biggest sphere
    static float sph(float r, float R, float h)
    {
     
        // the radii and height
        // cannot be negative
        if (r < 0 && R < 0 && h < 0)
            return -1;
     
        // radius of the sphere
        float x = r;
     
        // volume of the sphere
        float V = (float)(4 * 3.14f *
                    Math.Pow(r, 3)) / 3;
     
        return V;
    }
     
    // Driver code
    public static void Main()
    {
        float r = 5, R = 8, h = 11;
        Console.WriteLine(sph(r, R, h));
    }
}
 
// This code is contributed by Ryuga

Javascript

 
// javascript Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is inscribed
// within a frustum
 
     
// Function to find the biggest sphere
function sph(r , R , h)
{
 
    // the radii and height cannot be negative
    if (r < 0 && R < 0 && h < 0)
        return -1;
 
    // radius of the sphere
    var x = r;
 
    // volume of the sphere
    var V = ((4 * 3.14 * Math.pow(r, 3)) / 3);
 
    return V;
}
 
// Driver code
 var r = 5, R = 8, h = 11;
document.write(sph(r, R, h).toFixed(5));
 
// This code is contributed by Amit Katiyar
 

输出：

523.333