可内接在平截头体内接的正圆柱体内的最大球体
这里给定的是一个平截头体高度 h ，顶半径 r &底半径 R ，它描绘了一个右圆柱体，而右圆柱体又描绘了一个球体。任务是找到这个球体的最大可能体积。 举例:
Input: r = 5, R = 8, h = 11
Output: 523.333
Input: r = 9, R = 14, h = 20
Output:3052.08
逼近:让圆柱体的高度= H ，球体的半径= x 我们知道，圆台内接圆柱体的高度和半径分别等于圆台的高度和顶半径(这里请参考)。所以圆柱体的高度= h ，圆柱体的半径= r 。 同样，圆柱内接球体的半径等于圆柱的半径(请参考此处)，所以 x = r 。 所以，球体的体积， V = 4πr^3/3 。 以下是上述办法的实施:
C++
// C++ Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is inscribed
// within a frustum
#include <bits/stdc++.h>
using namespace std;
// Function to find the biggest sphere
float sph(float r, float R, float h)
{
// the radii and height cannot be negative
if (r < 0 && R < 0 && h < 0)
return -1;
// radius of the sphere
float x = r;
// volume of the sphere
float V = (4 * 3.14 * pow(r, 3)) / 3;
return V;
}
// Driver code
int main()
{
float r = 5, R = 8, h = 11;
cout << sph(r, R, h) << 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 sphere
// that can be inscribed within a right
// circular cylinder which in turn is inscribed
// within a frustum
import java.lang.Math;
class gfg
{
// Function to find the biggest sphere
static float sph(float r, float R, float h)
{
// the radii and height cannot be negative
if (r < 0 && R < 0 && h < 0)
return -1;
// radius of the sphere
float x = r;
// volume of the sphere
float V = (float)(4 * 3.14f * Math.pow(r, 3)) / 3;
return V;
}
// Driver code
public static void main(String[] args)
{
float r = 5, R = 8, h = 11;
System.out.println(sph(r, R, h));
}
}
// This Code is contributed by Code_Mech.
Python 3
# Python3 Program to find the biggest sphere
# that can be inscribed within a right
# circular cylinder which in turn is inscribed
# within a frustum
import math as mt
# Function to find the biggest sphere
def sph(r, R, h):
# the radii and height cannot
# be negative
if (r < 0 and R < 0 and h < 0):
return -1
# radius of the sphere
x = r
# volume of the sphere
V = (4 * 3.14 * pow(r, 3)) / 3
return V
# Driver code
r, R, h = 5, 8, 11
print(sph(r, R, h))
# This code is contributed by
# Mohit kumar 29
C
// C# Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is
// inscribed within a frustum
using System;
class gfg
{
// Function to find the biggest sphere
static float sph(float r, float R, float h)
{
// the radii and height
// cannot be negative
if (r < 0 && R < 0 && h < 0)
return -1;
// radius of the sphere
float x = r;
// volume of the sphere
float V = (float)(4 * 3.14f *
Math.Pow(r, 3)) / 3;
return V;
}
// Driver code
public static void Main()
{
float r = 5, R = 8, h = 11;
Console.WriteLine(sph(r, R, h));
}
}
// This code is contributed by Ryuga
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is
// inscribed within a frustum Function
// to find the biggest sphere
function sph($r, $R, $h)
{
// the radii and height
// cannot be negative
if ($r < 0 && $R < 0 && $h < 0)
return -1;
// radius of the sphere
$x = $r;
// volume of the sphere
$V = (4 * 3.14 * pow($r, 3)) / 3;
return $V;
}
// Driver code
$r = 5;
$R = 8;
$h = 11;
echo sph($r, $R, $h);
#This Code is contributed by ajit..
?>
java 描述语言
<script>
// javascript Program to find the biggest sphere
// that can be inscribed within a right
// circular cylinder which in turn is inscribed
// within a frustum
// Function to find the biggest sphere
function sph(r , R , h)
{
// the radii and height cannot be negative
if (r < 0 && R < 0 && h < 0)
return -1;
// radius of the sphere
var x = r;
// volume of the sphere
var V = ((4 * 3.14 * Math.pow(r, 3)) / 3);
return V;
}
// Driver code
var r = 5, R = 8, h = 11;
document.write(sph(r, R, h).toFixed(5));
// This code is contributed by Amit Katiyar
</script>
Output:
523.333
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