The spherical dome: Surface area and volume

The spherical dome is the figure resulting from having made a flat cut in a sphere.

The height and the maximum radius of the dome are related by the following expression with the radio of the sphere: $$R={\displaystyle \frac{r^2+h^2}{2h}}$$ The area and volume are calculated: $$\begin{gathered} A=2\pi \cdot R\cdot h \\ V={\displaystyle \frac{1}{3}}\pi \cdot h^2(3R-h) \end{gathered}$$