最大的右圆柱体，可以被内接在圆锥体中，而圆锥体又被内接在立方体中
这里给定的是一个边长为和的立方体，立方体上刻有一个圆锥体，圆锥体又刻有一个正圆柱体。任务是找到这个圆柱体的最大可能体积。 例:
Input: a = 5
Output: 232.593
Input: a = 8
Output: 952.699
逼近 : 从图中可以很清楚的看到，圆锥体的高度， H = a 和圆锥体的半径， R = a√2 ，请参考立方体内可内接的最大圆锥体。 和，圆柱体的半径， r = 2R/3 和圆柱体的高度， h = 2H/3 ，请参考可内接在圆锥体内的最大右圆柱体。 所以，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 。 所以，气缸的容积， V = 16πa^3/27 。 以下是上述方法的实施:
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 <bits/stdc++.h>
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 语言(一种计算机语言，尤用于创建网站)
// 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.
Python 3
# 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
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP 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
$r = (2 * $a * 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
$a = 5;
echo cyl($a);
// This code is contributed by Mahadev99
?>
java 描述语言
<script>
// 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
</script>
Output:
232.593
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