How can I fill the ring like this picture?

Question

I want to fill a ring like this picture

With Geogebra, I tried it by plot 4<=x^2+y^2<=9and this is the code in Geogebra

\documentclass[12pt]{standalone}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{patterns}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-3.3,-3.3) rectangle (3.3,3.3);
\draw [rotate around={0.:(0.,0.)},color=black] (0.,0.) ellipse (2.cm and 2.cm);
\draw [rotate around={0.:(0.,0.)},color=black,fill=black,fill opacity=0.1] (0.,0.) ellipse (3.cm and 3.cm);
\end{tikzpicture}
\end{document}

but, I got

How can I fill the ring as the firt picture?

Answer 1

A simple way to do this kind of operation is fill the center circle with fill=white, and to get the cross hatch fill pattern you use pattern=crosshatch:

Code

\documentclass[12pt]{standalone}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{patterns}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-3.3,-3.3) rectangle (3.3,3.3);
\draw [rotate around={0.:(0.,0.)},color=black] (0.,0.) ellipse (2.cm and 2.cm);
\draw [rotate around={0.:(0.,0.)},color=black,fill=black,fill opacity=0.1] (0.,0.) ellipse (3.cm and 3.cm);
\draw [rotate around={0.:(0.,0.)},color=black,fill=white] (0.,0.) ellipse (2.cm and 2.cm);
\end{tikzpicture}
% -------------------
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-3.3,-3.3) rectangle (3.3,3.3);
\draw [rotate around={0.:(0.,0.)},color=black] (0.,0.) ellipse (2.cm and 2.cm);
\draw [rotate around={0.:(0.,0.)},color=black,fill=black,fill opacity=0.5, pattern=crosshatch] (0.,0.) ellipse (3.cm and 3.cm);
\draw [rotate around={0.:(0.,0.)},color=black,fill=white] (0.,0.) ellipse (2.cm and 2.cm);
\end{tikzpicture}
\end{document}

Answer 2

Why all that typing?

\documentclass[border=5]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}
\draw[fill=gray!30,even odd rule]  (0,0) circle (3cm)
                                   (0,0) circle (2cm);
\end{tikzpicture}
% -------------------
\begin{tikzpicture}
\draw[even odd rule,pattern=crosshatch]  (0,0) circle (3cm)
                                         (0,0) circle (2cm);
\end{tikzpicture}
\end{document}