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: $$$R=\dfrac{r^2+h^2}{2h}$$$ The area and volume are calculated: $$$A=2\pi \cdot R \cdot h \\ V=\dfrac{1}{3}\pi \cdot h^2(3R-h)$$$