📜  球体中最大的右圆柱体的体积

📅  最后修改于: 2021-05-31 21:03:51             🧑  作者: Mango

给定半径范围R  。任务是找到可以在其中刻出的最大右圆柱的体积。
例子

Input : R = 4
Output : 77.3495


Input : R = 5
Output : 151.073

方法
r为右圆柱的半径, h为高度。
圆柱体的体积, V =π* r 2 * h
同样, r 2 = R 2 – h 2
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,V最大=2πR3 /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


PHP


Javascript


输出:
77.3495