3d plotting, washer integration, curve rotation, how to do it?

Questions
, , ,
1

I’m trying to create an illustration to accompany a math problem. The problem asks to rotate a region bounded by two curves about the y-axis (see image below).

I’m fairly new to using Cetz and Lilaq, and I’m struggling to find a starting point. Would anyone have any suggestions?

Goals:

  • plot the 2 curves
  • plot the surfaces they create/rotated volume
  • plot the infinitesimal volume cut out depicting large R and small r
  • add accompanying content/text

From what I’ve found, I would need to know how to plot the surface or its parametrization, and I’m wondering if there is an easier way.

image
image981×942 67.6 KB

2

I’m not sure if it’s possible to draw exactly what you want with it, but there’s a package called simple plot that has a function called volume-of-revolution. It takes a function as an argument and draws a volume by rotating it around the x-axis.

3

Personally i think doing it all in mathplotlib (python) and just saving the result as svg file (not converting) will be easier and fast. Maybe just add a semi transparent cylinder and the y^2 plot. (Or x^2+y^2)