可以内接在锥体内的最大直圆柱体，而锥体又内接在立方体内

这里给出是边长为a的立方体，其内接的锥体这反过来题直圆柱体。任务是找到这个圆柱体的最大可能体积。
例子：

Input: a = 5
Output: 232.593

Input: a = 8
Output: 952.699

方法：
从图中可以很清楚地看出，圆锥的高度， H=a ，圆锥的半径， R=a√2 ，请参考可在立方体内内切的最大圆锥。
并且，圆柱的半径r = 2R/3和圆柱的高度h = 2H/3 ，请参阅可内接在圆锥内的最大直圆柱。
因此，圆柱体相对于立方体的半径r = 2a√2/3和圆柱体相对于立方体的高度h = 2a/3 。
因此，圆柱体的体积V = 16πa^3/27 。
下面是上述方法的实现：

C++

// C++ Program to find the biggest right circular
// cylinder that can be inscribed within a right
// circular cone which in turn is inscribed
// within a cube
#include 
using namespace std;
 
// Function to find the biggest
// right circular cylinder
float cyl(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of right circular cylinder
    float r = (2 * a * sqrt(2)) / 3;
 
    // height of right circular cylinder
    float h = (2 * a) / 3;
 
    // volume of right circular cylinder
    float V = 3.14 * pow(r, 2) * h;
 
    return V;
}
 
// Driver code
int main()
{
    float a = 5;
    cout << cyl(a) << endl;
 
    return 0;
}

Java

// Java Program to find the biggest right circular
// cylinder that can be inscribed within a right
// circular cone which in turn is inscribed
// within a cube
import java.lang.Math;
 
class cfg
{
 
// Function to find the biggest
// right circular cylinder
static float cyl(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of right circular cylinder
    float r = (2 * a *(float)(Math.sqrt (2)) / 3);
 
    // height of right circular cylinder
    float h = (2 * a) / 3;
 
    // volume of right circular cylinder
    float V =(3.14f *(float)(Math.pow(r, 2) * h));
 
    return V;
}
 
// Driver code
public static void main(String[] args)
{
    float a = 5;
    System.out.println(cyl(a));
}
}
 
// This code is contributed by Mukul Singh.

Python3

# Python3 Program to find the biggest
# right circular cylinder that can be
# inscribed within a right circular
# cone which in turn is inscribed
# within a cube
import math as mt
 
# Function to find the biggest
# right circular cylinder
def cyl(a):
 
    # side cannot be negative
    if (a < 0):
        return -1
 
    # radius of right circular cylinder
    r = (2 * a * mt.sqrt(2)) / 3
 
    # height of right circular cylinder
    h = (2 * a) / 3
 
    # volume of right circular cylinder
    V = 3.14 * pow(r, 2) * h
 
    return V
 
# Driver code
a = 5
print(cyl(a))
 
# This code is contributed by
# Mohit kumar 29

C#

// C# Program to find the biggest
// right circular cylinder that can
// be inscribed within a right circular
// cone which in turn is inscribed
// within a cube
using System;
 
class GFG
{
 
    // Function to find the biggest
    // right circular cylinder
    static float cyl(float a)
    {
 
        // side cannot be negative
        if (a < 0)
            return -1;
 
        // radius of right circular cylinder
        float r = (2 * a * (float)(Math.Sqrt (2)) / 3);
 
        // height of right circular cylinder
        float h = (2 * a) / 3;
 
        // volume of right circular cylinder
        float V =(3.14f * (float)(Math.Pow(r, 2) * h));
        return V;
    }
 
    // Driver code
    public static void Main()
    {
        float a = 5;
        Console.Write(cyl(a));
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

 
// javascript Program to find the biggest right circular
// cylinder that can be inscribed within a right
// circular cone which in turn is inscribed
// within a cube
 
// Function to find the biggest
// right circular cylinder
function cyl(a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // radius of right circular cylinder
    var r = (2 * a *(Math.sqrt (2)) / 3);
 
    // height of right circular cylinder
    var h = (2 * a) / 3;
 
    // volume of right circular cylinder
    var V =(3.14 *(Math.pow(r, 2) * h));
 
    return V;
}
 
// Driver code
 
var a = 5;
document.write(cyl(a).toFixed(5));
 
// This code contributed by Princi Singh
 

输出：

232.593

如果您希望与专家一起参加现场课程，请参阅DSA 现场工作专业课程和学生竞争性编程现场课程。