球体内最大正圆柱体的体积

给定一个半径球体$R$ .任务是找到可以内接的最大正圆柱体的体积。
例子：

Input : R = 4
Output : 77.3495


Input : R = 5
Output : 151.073

方法：
令r为正圆柱的半径， h为其高度。
圆柱体的体积， V = π*r ² *h
此外， r ² = R ² – h ²
或者， V = π*(R ² – h ² )*h
或者， dV/dh = π*(R ² – 3*h ² )
将其设置为零，我们得到h = R/√3
所以， Vmax = 2πR ³ /3√3
下面是上述方法的实现：

C++

// C++ Program to find the biggest right circular cylinder
// that can be fit within a sphere
 
#include 
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

Javascript

 
// 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
 

输出：

77.3495