Cylinder Paraboloid

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\documentclass{article}
%
% File name: cylinder-paraboloid.tex
% Description:
% A solid bounded by the following surfaces
% z = 0
% z = x^{2} + y^{2}
% x^{2} + y^{2} = 1
% is generated. I.e., a paraboloid and a cylinder for x^2 + y^2 \leq 1, and z \geq 0.
% 
% 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}
\usetikzlibrary{math}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
\begin{document}
    %
    \tdplotsetmaincoords{60}{130}
    \begin{tikzpicture}[tdplot_main_coords,scale=0.75]
        \tikzmath{function f(\x) {return \x;};}
        \pgfmathsetmacro{\zini}{0.5*sqrt(2.0)}
        \pgfmathsetmacro{\step}{0.01}
        \pgfmathsetmacro{\zsig}{\zini+\step}
        \pgfmathsetmacro{\nextz}{\zini+0.5*\step}
        \pgfmathsetmacro{\sig}{2.0*\step}
        \pgfmathsetmacro{\tini}{0.5*pi}
        \pgfmathsetmacro{\tnext}{\tini+\step}
        \pgfmathsetmacro{\tfin}{1.85*pi}
        \pgfmathsetmacro{\tend}{2.5*pi}
        \pgfmathsetmacro{\tNext}{\tfin+\step}
 
 
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