graphics3d - How do I draw a hemisphere?

I want to draw a solid or partially transparent hemisphere above a partially transparent cuboid object in Graphics3D. However, I do not know how to do this such that only half the sphere is drawn. Here's what the object looks like with the full sphere:

SphereOpacity = 0.5;
CuboidOpacity = 0.5;
SphereColor = Blue;
CuboidColor = Orange;
Graphics3D[{SphereColor, Opacity[SphereOpacity], Sphere[{0, 0, 0.5}, 0.5], 
            CuboidColor, Opacity[CuboidOpacity], Cuboid[{-5, -5, 0}, {5, 5, 0.5}]}, 
            Boxed -> False
]

How might I proceed to "remove" the bottom half the sphere embedded in the cuboid primitive? In general, is there a way to not render/draw parts of a graphics primitive conditioned intersection with another primitive?

Answer

ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]}, 
                 {u, 0, π}, {v, 0, π},             
                 Mesh -> None, 
                 Boxed -> False, 
                 Axes -> None
]

r = 0.5;
d = {0, 0, 0.5}
sphere = ParametricPlot3D[r {Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]} + d, 
            {u, -π/2, π/2}, {v, -π/2, π/2}, 
            Mesh -> None, Boxed -> False, Axes -> None][[1]];

SphereOpacity = 0.5;
CuboidOpacity = 0.5;
SphereColor = Blue;

CuboidColor = Orange;
Graphics3D[{SphereColor, Opacity[SphereOpacity], sphere, CuboidColor, 
            Opacity[CuboidOpacity], Cuboid[{-5, -5, 0}, {5, 5, 0.5}]}, 
           Boxed -> False]