CodeForces 630Q：Pyramids【几何】

Pyramids
Time Limit:500MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u
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Description

IT City administration has no rest because of the fame of the Pyramids in Egypt. There is a project of construction of pyramid complex near the city in the place called Emerald Walley. The distinction of the complex is that its pyramids will be not only
quadrangular as in Egypt but also triangular and pentagonal. Of course the amount of the city budget funds for the construction depends on the pyramids' volume. Your task is to calculate the volume of the pilot project consisting of three pyramids — one triangular,
one quadrangular and one pentagonal.

The first pyramid has equilateral triangle as its base, and all 6 edges of the pyramid have equal length. The second pyramid has a square as its base and all 8 edges of the pyramid have equal length. The third pyramid has a regular pentagon as its base and
all 10 edges of the pyramid have equal length.



Input

The only line of the input contains three integers l3, l4, l5 (1 ≤ l3, l4, l5 ≤ 1000)
— the edge lengths of triangular, quadrangular and pentagonal pyramids correspondingly.

Output

Output one number — the total volume of the pyramids. Absolute or relative error should not be greater than 10 - 9.

Sample Input

Input

2 5 3

Output

38.546168065709

题意：给你正三棱锥，正四棱锥，正五棱锥的边长，让你求它们的体积和是多少。
思路：卡就卡在高上。。。。百度到的
正四面体 高

 底面积

 体积

 
正五面体 高

 底面积

 体积

 
正六面体 高

 底面积

 其中

 
体积


AC-code：

#include<cstdio>
#include<cmath>
#define PI acos(-1.0)
int main()
{
double a,b,c,s1,s2,s3,k,h1,h2,h3,v1,v2,v3;
scanf("%lf%lf%lf",&a,&b,&c);
h1=sqrt(6)*a/3;
s1=sqrt(3)*a*a/4;
v1=h1*s1/3;

h2=b/sqrt(2) ;
s2=b*b;
v2=h2*s2/3;

k=1/(2*tan(PI/10)*(1+cos(PI/5)));
h3=sqrt(1-k*k)*c;
s3=5*k*cos(PI/5)*c*c/2;
v3=h3*s3/3;
printf("%.10lf\n",v1+v2+v3);
return 0;
}