Answer
$x^2+y^2+z^2\leq4\space,\space z\geq0$
Work Step by Step
The formula of a sphere centered at the origin is $x^2+y^2+z^2=r^2$.
to find the upper half we restrict $z \geq 0$
to make it solid we change the $=$ to $\leq$
So the solid top half of a sphere centered at the origin with radius 2 is:
$$x^2+y^2+z^2\leq4\space,\space z\geq0$$
