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:

$$A=2\pi \cdot R \cdot h \\ V=\dfrac{1}{3}\pi \cdot h^2(3R-h)$$