Now that we have observed the areas formed by intersecting circles, the next logical
step is to observe the volumes formed by two intersecting spheres, each having
centerpoints at some coordinates (x1, y1, z1) and (x2, y2, z2) and both having
equal radii r.
What is the total area of the green region bounded by these intersecting spheres?
Problem Statement
Input Data
First line will be Q, the quantity of testcases.
Q lines will then follow, each holding a testcase in the format
r x1 y1 x1 x2 y2 z2 describing two intersecting spheres with radius r.
Answer
Should consists of Q space-separated values corresponding to the volume of the
region formed by the intersection of the two spheres described in each testcase.
Error should be less than 1e-3.
Example
input data:
1 0 0 0 1 0 0
21 -9 -8 -7 6 5 4
answer:
1.309 10411.400