# How to draw the band of a sphere using tikzpicture?

I would like to draw a scattering experiment. For this purpose I need to draw the band of a sphere. It seems rather complicated and my basic tikz skills are sadly not enough. If somebody has an input for me, please let me know. EDIT: I achieved the drawing of the spherical band using latitudes and rotating the picture 90 degrees. But how can I do the filling between the two latitudes like in my sketch?

     \begin{tikzpicture}

\newcommand\latitude{%
\draw[dashed] (#1:2) arc (0:-180:{2*cos(#1)} and {0.25*cos(#1)});
\draw (#1:2) arc (0:180:{2*cos(#1)} and {0.25*cos(#1)});
}

\begin{scope}[rotate around={90:(8,0)},shift={(8,0)}]
\draw[fill=black] (0,0) circle (0.1);
\draw[dashed] (0,0) circle (2);
\latitude{-20}
\latitude{-30}
\end{scope}
%
\end{tikzpicture}


Alternatively, you can use http://www.ctan.org/pkg/pst-solides3d

\documentclass{article}
\usepackage{tikz}
\usepackage{pst-solides3d}
\begin{document}

\begin{pspicture}
\psSolid[
object=calottesphere,
r=3,ngrid=16 18,
phi=20,theta=30,
hollow,RotY=-80]%
\end{pspicture}
\end{document}


Here's a proposition based on yours: just combine your arcs into one path and fill.

\newcommand\latitudes[]{%
\draw[dashed] (#2:2) arc (0:-180:{2*cos(#2)} and {0.25*cos(#2)});
\draw[dashed] (#3:2) arc (0:-180:{2*cos(#3)} and {0.25*cos(#3)});
\draw[#1] (#2:2) arc (0:180:{2*cos(#2)} and {0.25*cos(#2)})
arc (180-#2:180-#3:2)
arc (180:0:{2*cos(#3)} and {0.25*cos(#3)})
arc (#3:#2:2);}

\begin{tikzpicture}

\begin{scope}[rotate around={90:(8,0)},shift={(8,0)}]
\draw[fill=black] (0,0) circle (0.1);
\draw[dashed] (0,0) circle (2);

\latitudes[fill=yellow]{-20}{-30}

\end{scope}
%
\end{tikzpicture} 