Cup

Cup

Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 932 Accepted Submission(s): 319

Problem Description

The WHU ACM Team has a big cup, with which every member drinks water. Now, we know the volume of the water in the cup, can you tell us it height?

The radius of the cup's top and bottom circle is known, the cup's height is also known.

 

Input

The input consists of several test cases. The first line of input contains an integer T, indicating the num of test cases.
Each test case is on a single line, and it consists of four floating point numbers: r, R, H, V, representing the bottom radius, the top radius, the height and the volume of the hot water.

Technical Specification

1. T ≤ 20.
2. 1 ≤ r, R, H ≤ 100; 0 ≤ V ≤ 1000,000,000.
3. r ≤ R.
4. r, R, H, V are separated by ONE whitespace.
5. There is NO empty line between two neighboring cases.

 

Output

For each test case, output the height of hot water on a single line. Please round it to six fractional digits.

 

Sample Input

1
100 100 100 3141562

 

Sample Output

99.999024

 

Source

The 4th Baidu Cup final

 

Recommend

lcy

/*
一晚上把底半径和二分的右区间变量名用重了，还看出来，真是.....
*/
#include<bits/stdc++.h>
#define op 1e-9
#define pi acos(-1.0)
using namespace std;
/*
V=π×h×(R2﹢R×r﹢r2)/3  
*/
double S(double r,double R,double h,double H)//圆台面积
{
    double r1=r+h*(R-r)/H;
    return pi*h*(r1*r1+r1*r+r*r)/3; 
}
int main()
{
    //freopen("C:\\Users\\acer\\Desktop\\in.txt","r",stdin);
    int t;
    double left,right,h,v;
    double r,R,H,V;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lf%lf%lf%lf",&r,&R,&H,&V);
        //cout<<r<<" "<<R<<" "<<H<<" "<<(int )V<<endl;
        left=0,right=100;
        while(right-left>op)
        {
            //cout<<h<<endl;
            h=(right+left)/2;
            v=S(r,R,h,H);
            //cout<<v<<endl;
            if(fabs(v-V)<=op)
                break;
            else if(v>V)
                right=h-op;
            else
                left=h+op;
        }
        printf("%.6lf\n",h);
    }
    return 0;
}