light oj 1216 - Juice in the Glass (几何计算)

1216 - Juice in the Glass

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Time Limit: 2 second(s)Memory Limit: 32 MB

Once upon a time, there lived a mad programmer. He loved to solve creative problems other than anything. His wife loved him quite a lot but disliked his curiosity for the problems. One day he came from office, his wife gave him a glass of cold lime juice. She was in a romantic mood and waiting for some romantic stuff. But the programmer asked her curiously, "If I give u radius of the top and bottom part of the glass and the height, can you come up with the volume of the glass?" His wife became a bit disappointed but as she is smart she replied with a smile, "You already have drunk some juice, and the glass is not full. If I give you the height of the juice, can you find the volume of the remaining juice in the glass?" Then the programmer kissed his wife and said, "You are the best problem setter in the world!"

Now he set the same problem for you. The radius of the upper part r₁ and lower part r₂ is given. If height of the glass is h and height of the juice is p what is the volume of the juice in the glass?

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing four integers r₁ r₂ h p (1 ≤ r₂ < r₁ ≤ 100, 1 ≤ p ≤ h ≤ 100).

Output

For each case, print the case number and the volume of the juice in the glass. Errors less than 10^-6 will be ignored.

Sample Input

Output for Sample Input

2

5 2 3 2

5 2 3 3

Case 1: 58.643062867

Case 2: 122.52211349

 解：求图中盛有水的部分的面积，设中间水平面圆的半径为r ， p/h=(r-r1)/(r1-r2)

圆台体积公式：v=(1.0/3)*H*(s1+s2+sqrt(s1*s2)//s1,s2分别是上下底面的面积

代码：

#include <iostream>#include <cstdio>#include <cmath>#define PI acos(-1)using namespace std;int main(){    int t,k=1;    double r1,r2,r,h,p;    double s1,s2,v;    scanf("%d",&t);    while(t--)    {        scanf("%lf%lf%lf%lf",&r1,&r2,&h,&p);        r=(r1-r2)*(p/h)+r2;    //三角形相似            s1=PI*r*r;        s2=PI*r2*r2;        v=(1.0/3)*p*(s1+s2+sqrt(s1*s2));//注意三分之一要写成1.0，不然结果就是0了               printf("Case %d: %.7lf\n",k++,v);    }    return 0;}