Image: Half spherical shell dome
The dome region consists of the upper half of a spherical shell with radius from 3 to 5, i.e.,the region is given by
\begin{gather*}
9 \le x^2 + y^2 + z^2 \le 25\\
z \ge 0.
\end{gather*}
Image file: dome_half_spherical_shell.png
Source image file: dome_half_spherical_shell.nb
Source image type: Mathematica