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?

The function $\varphi:B(0,1)\to\mathbb{R}^3$ given by 
$$\varphi(x,y)=\left(x,y,\sqrt{4-x^2-y^ 2}\right)$$ 
will parametrize your surface, where $B(0,1)=\{(x,y)\in\mathbb{R}^2|x^2+y^2\leq 1\}$.
