1216 - Juice in the Glass

       You have to know about Volume of frustum of a cone . We will discuss a little bit about this . Hope after that you will get a complete idea about this 

          
          A frustum (unfortunately commonly misspelled "frustrum") is that portion of a solid which lies between two parallel planes cutting the solid. Degenerate cases are obtained for finite solids by cutting with a single plane only.         
        
         A frustum may be formed from a cone with a circular base by cutting off the tip of the cone with a cut perpendicular to the height, forming a lower base and an upper base that are circular and parallel.
       
         Let h be the height, R the radius of the lower base, and r the radius of the upper base. One picture of the frustum is the following.

        The main problem is "Given R, r, and h, find the volume of the frustum. " The formula is  ,

Now lets come back to the main problem of light online judge :



                                            


It is slightly a different version of our discussion .  As we have to find the volume of only coloured space of the glass , the formula is as following :

If                R1 =  r1 .
                  R2 = r2 + (r1-r2)*p/h
                  H=p

The the volume of colured glass is V = 1/3 * H * ( R1*R1 + R2*R1 + R2*R2 )

Hope after this discussion all things are very much clearer to you . Have a great day .               

Code :

#include<iostream>
#include<cmath>
#include<cstdio>
using namespace std;

#define PI acos(-1)

int main()
{
    int i,test,r1,r2,h,p;
    double R,V;
    cin>>test;
    for(i=1;i<=test;i++)
    {
        cin>>r1>>r2>>h>>p;
        R= r2 + (r1-r2)*(double(p)/h);
        V = 1/3.0 * PI * p *( R*R + R*r2 + r2*r2 );
        printf("Case %d: %lf\n",i,V);
    }
    return 0;
}