/sci/ - Science & Math

Hey guys. I'm solving a problem but having trouble. I've finished the question but I dont understand one thing;

The problem is basically just find the volume of half a sphere, where the cords of xyz are all in the origin, radius of the sphere is 1. The instructions say that integrating both x and y will result in 0 so there's no point, hence I have to integrate in spherical cords around z. Why is that? Why will it be zero? I understand the symmetry but it's a spherical shape, how will its volume ever end up zero?