Nonconvex Solid

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\documentclass{article}
%
% File name: nonconvex-solid.tex
% Description: 
% The solid bounded by the graphs of the surfaces:
% z = 1 - x^{2} - y^{2}
% z = 1
% x^2 + y^2 = 1
% is generated. Also, the region x^2 + y^2 \leq 1
% is shown.
% 
% Date of creation: April, 23rd, 2022.
% Date of last modification: April, 23rd, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% 
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
\begin{document}
    %
    \tdplotsetmaincoords{60}{110}
    \begin{tikzpicture}[tdplot_main_coords,scale=2.0]
        \pgfmathsetmacro{\tini}{0.5*pi}
        \pgfmathsetmacro{\tfin}{1.85*pi}
        \pgfmathsetmacro{\tend}{2.5*pi}
        \pgfmathsetmacro{\final}{2.0*pi}
        \coordinate (A) at (1.25,1.25,1);
        \coordinate (B) at (-1.25,1.25,1);
        \coordinate (C) at (-1.25,-1.5,1);
        \coordinate (D) at (1.25,-1.5,1);
        % Node indicating the equation of the circumference
        \draw[white] (1.35,0,0) -- (0,1.35,0) node [black,below,midway,sloped] {$x^2 + y^2 = 1$};
        %%% Coordinate axis
 
 
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