# Cylinder Truncated by Plane

Edit and compile if you like:

\documentclass{article}
%
% File name: cylinder-truncated-by-plane.tex
% Description:
% A solid bounded by the following surfaces
% z = 0
% x^{2} + y^{2} = 4
% x + y + z = 4
% is generated. I.e., the intersection of a cylinder with a plane
% for z >= 0.
%
% Date of last modification: April, 23rd, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% According to TikZ.net
%
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
\begin{document}
%
\tdplotsetmaincoords{60}{110}
\begin{tikzpicture}[tdplot_main_coords,scale=0.65]
\tikzmath{function a(\x,\y) {return (4.0-\x-\y);};}
\pgfmathsetmacro{\final}{2.0*pi}
\pgfmathsetmacro{\ejez}{a(0,0)}
% The equation of the cyrcumference
\draw[white] (0,-2.5,0) -- (2.75,0,0) node[blue,midway,below,sloped] {\footnotesize$x^2 + y^2 = 4$};
% The region of integration: the circle of radius 2
\draw[thick,fill=yellow,opacity=0.5] plot[domain=0:6.2832,smooth,variable=\t] ({2.0*cos(\t r)},{2.0*sin(\t r)},{0.0});
%%% Coordinate axis
\draw[thick,->] (0,0,0) -- (3.5,0,0) node [below left] {\footnotesize$x$};
\draw[dashed] (0,0,0) -- (-3,0,0);
\draw[thick,->] (0,0,0) -- (0,3.5,0) node [right] {\footnotesize$y$};
\draw[dashed] (0,0,0) -- (0,-3,0);
\draw[thick] (0,0,0) -- (0,0,\ejez);% node [above] {\footnotesize$z$};
% The plane: x + y + z = 4
\pgfmathsetmacro{\Az}{a(2.5,2.5)}
\pgfmathsetmacro{\Bz}{a(-2.5,2.5)}
\pgfmathsetmacro{\Cz}{a(-2.5,-2.5)}
\pgfmathsetmacro{\Dz}{a(2.5,-2.5)}
\coordinate (A) at (2.5,2.5,\Az);
\coordinate (B) at (-2.5,2.5,\Bz);
\coordinate (C) at (-2.5,-2.5,\Cz);
\coordinate (D) at (2.5,-2.5,\Dz);
% The cylinder
\foreach \angulo in {0,0.01,...,\final}{
\pgfmathparse{2.0*cos(\angulo r)}
\pgfmathsetmacro{\px}{\pgfmathresult}
\pgfmathparse{2.0*sin(\angulo r)}
\pgfmathsetmacro{\py}{\pgfmathresult}
\draw[cyan,opacity=0.5] (\px,\py,0) -- (\px,\py,4.0-\px-\py);
}
% The intersection of the cylinder and the plane (the trace)
\draw[blue,thick] plot[domain=0:6.2832,smooth,variable=\t] ({2.0*cos(\t r)},{2.0*sin(\t r)},{4.0-2.0*sin(\t r)-2.0*cos(\t r)});
% Circumference & Ellipse bounding the solid.
\draw[blue,thick,opacity=0.5] plot[domain=0:6.2831853,smooth,variable=\t] ({2.0*cos(\t r)},{2.0*sin(\t r)},{4.0-2*sin(\t r)-2.0*cos(\t r)});
\draw[blue,thick,opacity=0.5] plot[domain=0:6.2831853,smooth,variable=\t] ({2.0*cos(\t r)},{2.0*sin(\t r)},{0.0});
% The plane
\draw[white] (C) -- (B) node[red,above,sloped,midway]{\footnotesize$x + y + z = 4$};
\draw[red,dash dot] (A) -- (B) -- (C)	 -- (D) -- (A);
\fill[pattern color=pink,pattern=north east lines] (A) -- (B) -- (C)	 -- (D) -- (A);
\fill[pink,opacity=0.5] plot[domain=0:6.2832,smooth,variable=\t] ({2.0*cos(\t r)},{2.0*sin(\t r)},{4.0-2.0*sin(\t r) - 2.0*cos(\t r)});
% z axis (last part)
\draw[thick,->] (0,0,\ejez) -- (0,0,8) node [above] {\footnotesize$z$};
\end{tikzpicture}
\end{document}