it is just combining two pictures, one is using tikz-3dplot the other is just tikz. This is the code. I want the picture to be side to side, left and right. I usually use \begin{scope}..\end{scope but this time the code is completely different with one is 3D and another just 2D.
3D code:
\documentclass[border=2mm,12pt,tikz]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d,calc,backgrounds}
\usepackage{fouriernc}
%% smuggling from https://tex.stackexchange.com/a/470979/121799
\newcounter{smuggle}
\DeclareRobustCommand\smuggleone[1]{%
\stepcounter{smuggle}%
\expandafter\global\expandafter\let\csname smuggle@\arabic{smuggle}\endcsname#1%
\aftergroup\let\aftergroup#1\expandafter\aftergroup\csname smuggle@\arabic{smuggle}\endcsname
}
\DeclareRobustCommand\smuggle[2][1]{%
\smuggleone{#2}%
\ifnum#1>1
\aftergroup\smuggle\aftergroup[\expandafter\aftergroup\the\numexpr#1-1\aftergroup]\aftergroup#2%
\fi
}
\begin{document}
% please do not use \x and \y since these are used in the calc syntax
\def\myx{1}
\def\myy{3}
\def\h{6}
\tdplotsetmaincoords{83}{70}
\begin{tikzpicture}[tdplot_main_coords]
% \draw[-latex] (0,0,0) -- (1,0,0) node[pos=1.1]{$x$};
% \draw[-latex] (0,0,0) -- (0,1,0) node[pos=1.1]{$y$};
% \draw[-latex] (0,0,0) -- (0,0,1) node[pos=1.1]{$z$};
\begin{scope}[canvas is xz plane at y=0]
\draw[thick] (0,0) coordinate[label=above:$$] (O) circle (\myy);
\end{scope}
\begin{scope}[canvas is xz plane at y=\h]
\path (0,0) coordinate[label=above:$$] (O');
\draw[thick] let \p1=($(O')-(O)$),\n1={atan2(\y1,\x1)} in
\pgfextra{\pgfmathsetmacro{\myangle}{\n1}\smuggle{\myangle}}
($(O)+({90+\n1}:\myy)$) --
({90+\n1}:\myy) arc({90+\n1}:{-90+\n1}:\myy) --
($(O)+({-90+\n1}:\myy)$) ;
\begin{scope}[on background layer,every label/.append style={black}]
\draw[dashed] ({90+\myangle}:\myy) arc({90+\myangle}:{180+90+\myangle}:\myy);
% front
\shade[top color=blue!30,bottom color=blue,shading angle=\myangle]
($(O)+({-20}:\myy)$) -- ($(O')+({-20}:\myy)$)
arc(-20:-90+\myangle:\myy) --($(O)+({-90+\myangle}:\myy)$)
arc(-90+\myangle:-20:\myy);
% left
\shade let \p1=($({-160}:\myy)-({-20}:\myy)$),\n1={180+atan2(\y1,\x1)} in
[top color=blue!30,bottom color=blue,shading angle=\n1]
($(O)+({-20}:\myy)$) arc(-20:-160:\myy) -- cycle;
%top
\fill[blue!20] ($(O')+({-20}:\myy)$) coordinate[label=right:$$](B')
-- ($(O')+({-160}:\myy)$) coordinate[label=above left:$$](A')
-- ($(O)+({-160}:\myy)$) coordinate[label=left:$$](A)
-- ($(O)+({-20}:\myy)$) coordinate[label=right:$$](B)
-- cycle;
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}
The 2D code:
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[scale=1,>=latex,x=1cm,y=0.8cm]
\draw (0,0) ellipse (4 and 4);% a circle
\draw[fill=blue!7] (-4,0) arc (180:360:4 and 4);% left half of the circle starting at (-4,0) from 180 to 360
\draw[fill=blue!37] ({sqrt(12)},-2) -- (-{sqrt(12)},-2) -- (-{sqrt(9.75)},-2.5) -- ({sqrt(9.75)},-2.5) -- cycle;
\draw [decorate,decoration={brace,amplitude=8pt},xshift=0.4pt,yshift=0.7pt]
(0.2,-1.9) -- (3.4,-1.9) node [black,above, midway,xshift=-0.6cm]
{$$};
\draw (2,-1.1) node {$\sqrt{16 - y^{2}}$};
\draw (4.1,4.2) node {$x^{2} + y^{2} = 16$};
\draw (-0.6,4.3) node {$(0,4)$};
\draw (4.5,0.3) node {$(4,0)$};
\draw[<->] (-4.2,0) -- (-4.2,-2) node[left, midway] {\footnotesize $-y$};
\draw[<->] (3.8,-2) -- (3.8,-2.5) node[right, midway] {\footnotesize $\triangle y$};
\draw[->,thick] (-5,0) -- (6,0) node[above] {\footnotesize $x$};
\draw[->,thick] (0,-5) -- (0,6) node[below right]{\footnotesize $y$};
\end{tikzpicture}
\end{document}
