Shaded hemisphere in perspective using PGF/TikZ

Example3.tex

\documentclass[crop=true, border=10pt]{standalone}

 
\usepackage{xcolor}

\usepackage{tikz}
\usetikzlibrary{arrows.meta}


% Some colors I like. The first six are modified versions of colors from
% the Gnome Project "Tango" palette.
\definecolor{plum}{rgb}{0.36078, 0.20784, 0.4}
\definecolor{chameleon}{rgb}{0.30588, 0.60392, 0.023529}
\definecolor{cornflower}{rgb}{0.12549, 0.29020, 0.52941}
\definecolor{scarlet}{rgb}{0.8, 0, 0}
\definecolor{brick}{rgb}{0.64314, 0, 0}
\definecolor{sunrise}{rgb}{0.80784, 0.36078, 0}
\definecolor{lightblue}{rgb}{0.15,0.35,0.75}
\definecolor{carolina}{RGB}{153, 186, 221}

% A custom arrowhead for use on x, y, z axes
\tikzstyle{axisarrow} = [-{Latex[inset=0pt,length=5pt]}]

\begin{document}

\begin{tikzpicture}[scale=1.2]
	% Draw the background grid.
	\draw [cornflower!20,step=0.25,thin] (-3,-3) grid (3,3);
	\draw [cornflower!40,step=1.0,thin] (-3,-3) grid (3,3);

	
	% The obscured part of the z-axis
	\draw (0,0) -- (0,-3);

	% Draw a shaded ball, but clip so only the lower half shows.
	% The arc in the clipping region is the foreground part of the equator
	\begin{scope}
	    \clip(-3,-3) -- (-3,0) -- (-2,0) arc (180:360:2cm and 0.6cm) -- (3,0) -- (3,-3) -- (-3,-3);
		\shade[ball color=chameleon!60!white, opacity=0.70] (0,0) circle (2cm);
	\end{scope}

	% Draw the disc on top of the hemisphere.
    \shade[shading=radial, inner color=chameleon!20!white, outer color=chameleon!60!white, opacity=0.70] (2,0) arc (0:360:2cm and 0.6cm); 
	
	% Outline the disk in black
    \draw (2,0) arc (0:360:2cm and 0.6cm);

	% Outline the hemisphere in black
    \draw (-2,0) arc (180:360:2cm and 2cm);

	% A dashed line and label indicating the radius
    \draw [dashed] (0,0)--(2,0);
	\node at (1.2,.2) {$R$};

	% The rest of the z-axis
	\draw[axisarrow] (0,0) -- (0,3);
	\node at (.2,2.8) {$z$};

	% The y-axis
	\draw[axisarrow] (-2.5,1) -- (2.5,-1);
	\node at (2.5,-1.2) {$y$};

	% The x-axis
	\draw[axisarrow] (2.5,1) -- (-2.5,-1);
	\node at (-2.5,-0.8) {$x$};

\end{tikzpicture}	

\end{document}