Find the volume of the solid that lies in between both of the spheres:
This is the first chapter of the calculus III material so no double or triple integrals are needed to solve this problem.
The Attempt at a Solution
I completed the square on the first equation and obtained:
So I just have 2 intersecting spheres. Finding the volume of a "slice" of a sphere can be done using a solid of revolution, however, I would need know how far one sphere is intersecting into the other in order to calculate the volume.
My idea is to minimize the distance between (x+2)2+(y-2)2+(z+2)2=4 and the point (0,0,0). Then I will be able to figure out how "thick" the 2 "slices" of the spheres are.
However, I'm not quite sure how to do this. I know how to find the distance between points in space but solving for each variable I will wind up with 2 solutions because of the radical. Is there an easier way to do this that I am missing?