It really isn't clear what you've tried or what the problem is. This
is almost, therefore, a do-it-for-me and I, therefore, hold that I
shouldn't answer it.
As a do-it-for-me, remaining adjustments are left entirely as an
exercise for the reader. I will be less sympathetic to requests for
fine-tuning and explanation than I would otherwise be.
I answer do-it-for-mes strictly for me. If it happens to be useful,
so be it. If not, so be it.
The most useful code you said you found is for a question where the answer does not even use TikZ. I'm not clear whether you were aware of this or not ....
\documentclass[border=10pt,tikz]{standalone}
\usetikzlibrary{arrows.meta}
\begin{document}
\begin{tikzpicture}
\draw [fill=gray, fill opacity=.25]
(180:5mm) coordinate (a)
-- ++(0,-12.5mm) coordinate (b)
arc (180:360:5mm and 1.75mm) coordinate (d)
-- (a -| d) coordinate (c) arc (0:180:5mm and 1.75mm);
\draw [fill=gray, fill opacity=.25]
(0,0) coordinate (t) circle (5mm and 1.75mm);
\draw [densely dashed] (d) arc (0:180:5mm and 1.75mm);
\draw []
(180:7.5mm) coordinate (A)
-- ++(0,-12.5mm) coordinate (B) node [midway, right, inner sep=1pt] {$v$}
arc (180:360:7.5mm and 2.625mm) coordinate (D)
-- (A -| D) coordinate (C) arc (0:180:7.5mm and 2.625mm);
\draw []
(0,0) coordinate (T) circle (7.5mm and 2.625mm);
\draw [densely dashed] (D) arc (0:180:7.5mm and 2.625mm);
\draw [densely dashed ]
([yshift=-12.5mm]T) coordinate (B)
edge [-Latex] node [pos=1, right] {$y$} +(-30:7.5mm)
edge [-Latex] node [pos=1, left] {$x$} +(-150:7.5mm)
-- (T) node [midway, right, anchor=west, fill=white, inner sep=.5pt] {$w$} node [anchor=center, circle, draw, solid, inner sep=.5pt, fill=white] {} edge [solid, -Latex] node [right, pos=1] {$z$} ++(0,5mm) ;
\end{tikzpicture}
\end{document}

lines plus arrowsrather thanaxes. – cfr Mar 26 '17 at 00:53