I've been given the metric spaces R^3 and S^2=\{(x,y,z) | x^2+y^2+z^2=1\} And i need to find the diameter of A which is A\subseteq S^2\subseteq R^3 Where A^2=\{(x,y,z) \in S^2 | z>0\}

I'm thinking that since S^2 is the unit-sphere and z has to be greater than 0, its down to half the unitsphere, thus making the diameter 2?. But im not sure on how to show it.