可被内接在球体中的最大右圆锥，该球体被内接在立方体中
给定一个边长为 a 的立方体，它刻制一个球体，球体又刻制一个直角圆锥。任务是找到这个圆锥体的最大可能体积。 例:
Input: a = 5
Output: 58.1481
Input: a = 8
Output: 238.175
逼近 : 让，右圆锥的高度= h 。 圆锥体的半径= r 球体的半径= R 我们，知道立方体内部球体的半径， r = a/2 。请参考(立方体内可内切的最大球体)。 同样，球体内部圆锥体的高度， h = 4r/3 。 球体内部的圆锥半径， r = 2√2r/3 。请参考(球面内可内切的最大右圆锥)。 因此，球体内部的圆锥体的高度依次内接在立方体内， h = 2a/3 。 球体内部的圆锥体半径，该球体又内接在立方体内， r = √2a/3 。 以下是上述方法的实施:
C++
// C++ Program to find the biggest right circular cone
// 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 cone
float cone(float a)
{
// side cannot be negative
if (a < 0)
return -1;
// radius of right circular cone
float r = (a * sqrt(2)) / 3;
// height of right circular cone
float h = (2 * a) / 3;
// volume of right circular cone
float V = 3.14 * pow(r, 2) * h;
return V;
}
// Driver code
int main()
{
float a = 5;
cout << cone(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 cone
// that can be inscribed within a right circular cone
// which in turn is inscribed within a cube
import java.io.*;
class GFG
{
// Function to find the biggest right circular cone
static float cone(float a)
{
// side cannot be negative
if (a < 0)
return -1;
// radius of right circular cone
float r = (float) (a * Math.sqrt(2)) / 3;
// height of right circular cone
float h = (2 * a) / 3;
// volume of right circular cone
float V = (float)(3.14 *Math. pow(r, 2) * h);
return V;
}
// Driver code
public static void main (String[] args)
{
float a = 5;
System.out.println( cone(a));
}
}
// This code is contributed by anuj_67..
Python 3
# Python3 Program to find the biggest right
# circular cone that can be inscribed within
# a right circular cone which in turn is
# inscribed within a cube
import math
# Function to find the biggest
# right circular cone
def cone(a):
# side cannot be negative
if (a < 0):
return -1;
# radius of right circular cone
r = (a * math.sqrt(2)) / 3;
# height of right circular cone
h = (2 * a) / 3;
# volume of right circular cone
V = 3.14 * math.pow(r, 2) * h;
return V;
# Driver code
a = 5;
print(cone(a));
# This code is contributed by
# Shivi_Aggarwal
C
// C# Program to find the biggest
// right circular cone 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 cone
static double cone(double a)
{
// side cannot be negative
if (a < 0)
return -1;
// radius of right circular cone
double r = (double) (a * Math.Sqrt(2)) / 3;
// height of right circular cone
double h = (2 * a) / 3;
// volume of right circular cone
double V = (double)(3.14 * Math.Pow(r, 2) * h);
return Math.Round(V,4);
}
// Driver code
static void Main ()
{
double a = 5;
Console.WriteLine(cone(a));
}
}
// This code is contributed by chandan_jnu
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the biggest right
// circular cone that can be inscribed
// within a right circular cone which in
// turn is inscribed within a cube
// Function to find the biggest
// right circular cone
function cone($a)
{
// side cannot be negative
if ($a < 0)
return -1;
// radius of right circular cone
$r = ($a * sqrt(2)) / 3;
// height of right circular cone
$h = (2 * $a) / 3;
// volume of right circular cone
$V = 3.14 * pow($r, 2) * $h;
return $V;
}
// Driver code
$a = 5;
echo round(cone($a), 4);
// This code is contributed by Ryuga
?>
java 描述语言
<script>
// javascript Program to find the biggest right circular cone
// that can be inscribed within a right circular cone
// which in turn is inscribed within a cube
// Function to find the biggest right circular cone
function cone(a)
{
// side cannot be negative
if (a < 0)
return -1;
// radius of right circular cone
var r = (a * Math.sqrt(2)) / 3;
// height of right circular cone
var h = (2 * a) / 3;
// volume of right circular cone
var V = (3.14 *Math. pow(r, 2) * h);
return V;
}
// Driver code
var a = 5;
document.write( cone(a).toFixed(5));
// This code is contributed by Amit Katiyar
</script>
Output:
58.1481
版权属于：月萌API www.moonapi.com，转载请注明出处
