Hello Yvette.
A sphere's equation centered at the position (a,b,c) with radius r is
(xa)^{2} + (yb)^{2} + (zc)^{2} = r^{2}
So a full sphere of radius 2 and centre point (3,1,0) is
(x3)^{2} + (y1)^{2} + z^{2} = 2^{2}
When you solve this for z, you get
z = sqrt(4  ((x3)^{2} + (y1)^{2}) ) or z =  sqrt(4  ((x3)^{2} + (y1)^{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  ((x3)^{2} + (y1)^{2}) ).
If you intended a solid sphere, rather than the shell, then change the first equation to
 sqrt(4  ((x3)^{2} + (y1)^{2}) ) ≤ z ≤ 0
Hope this helps,
Stephen and Penny.
