For $0<h<r$ there is a surface $$C=\{(x,y,z)\in\mathbb{R}^3:x^2+y^2+z^2=r^2, z\geq h\}$$
I know that area$=\int\int_C1dS=\int\int_D|R_u\times R_v|dA$, where $R$ is my parametrization and $D$ the domain of parametrization.
Is $R(\phi,\theta)=(h\sin\phi\cos\theta,h\sin\phi\sin\theta,h\cos\phi)$ a good parametrization? And if so, what are the boundaries of $\phi$ and $\theta$?
Edit:Or should I use spherical coordinates (and again what would the boundaries be in that case?)
We use spherical coordinates, then the area $A$ is $$A=\int_{\theta=0}^{2\pi}\int_\phi r^2\sin\phi d\phi d\theta=\int_{\theta=0}^{2\pi}\int_{z=r}^h -rd\theta dz=\int_{\theta=0}^{2\pi}\int_{z=h}^r rd\theta dz=2\pi r(r-h).$$