可以刻在截头圆锥体上刻在右圆柱上的最大球体

这里给出的是一个高度为h的平截头体，顶部半径r和底部半径R内接一个右圆柱，内圆柱又接一个球。任务是找到该球体的最大体积。
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，截头圆锥体内的圆柱体的高度和半径分别等于截头圆锥体的高度和顶部半径(请参阅此处)，因此圆柱体的高度= h ，圆柱体的半径= r 。
另外，圆柱内接球的半径等于圆柱的半径(请参阅此处)，因此x = r 。
因此，球的体积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