A sphere's equation centered at the position (a,b,c) with radius r is
(x-a)2 + (y-b)2 + (z-c)2 = r2
So a full sphere of radius 2 and centre point (3,1,0) is
(x-3)2 + (y-1)2 + z2 = 22
When you solve this for z, you get
z = sqrt(4 - ((x-3)2 + (y-1)2) ) or z = - sqrt(4 - ((x-3)2 + (y-1)2) )
If z is the up/down axis, then you only want z < 0 if you want just the "lower half" of the sphere, that is
z = - sqrt(4 - ((x-3)2 + (y-1)2) ).
If you intended a solid sphere, rather than the shell, then change the first equation to
- sqrt(4 - ((x-3)2 + (y-1)2) ) ≤ z ≤ 0
Hope this helps,
Stephen and Penny.