Drawing a funnel with Tikz

Question

Does anyone have a method for drawing a funnel in Tikz?

I am attempting to replicate the funnel drawn for this past year's AP Calculus BC free-response questions.

I have attached the image that I would like to recreate using Tikz below.

Any help would be much appreciated!

Answer 1

Here is a starting point. You should be able to adjust this easily by reading the TikZ manual.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \foreach \sgn in {-,+}
    \draw plot[domain=0:10] ({\sgn 1/20*(3+\x*\x)},\x);
  \foreach \h in {0,5,10}
    \draw (0,\h) ellipse[x radius=1/20*(3+\h*\h),y radius=(\h+.5)/20];
  \draw (0,0) -- node[right] {$h$} (0,5);
  \draw (0,5) -- node[above] {$r$} ({-1/20*(3+5*5)},5);
\end{tikzpicture}
\end{document}