What kind of surface is this? Is there a way to plot this? I am given the surface:
$$S=\{ \vec{x} \in \mathbb R^3: {\|\vec{x} \|}_2^2=4, x^2+y^2 \le 1, z >0 \}$$
and I want to calculate the Mass of $S$ given a density $\rho$. It sort of looks like the upper half of a sphere. The problem I have is that the first equation ${\| \vec{x} \|}_2^2=4$ means that the radius of this sphere is $R=2$. 
However, the condition $x^2+y^2 \le1$ would mean that it is some kind of half sphere with a smaller "base". I tried to plot this in Wolfram Alpha but I couldn't get it to work.
Is there any way I can parameterize/transform this surface in spherical coordinates?

In spherical coordinates (warning: notations may differ)
$$ \eqalign{x &= r \sin (\theta) \cos (\phi)\cr
            y &= r \sin (\theta) \sin(\phi)\cr
            z &= r \cos(\theta)}$$
you have $\|\vec{x}\| = r$ and $x^2 + y^2 = r^2 \sin^2(\theta)$, so in this case
you want $r = 2$ and $0 \le \theta \le \arcsin(1/2) = \pi/6$.
