# Instructions - Washington and Lee University

```How to create a Volume by Cylindrical Shells in Cinema 4D
1. The Math
a. Determine the number of cylindrical shells you will use, say n.
b. Volumes of revolution are given, for example, by rotating an area from x=a to
𝑏−𝑎
x=b about the y-axis. The thickness of each shell is then 𝑛 .
c. Find the height of each shell from the given function(s). You can use a right,
left, or midpoint approximation.
2. Open Cinema 4D.
shell.
a. Determine the outer and inner radii for each shell (that is, the distance from
the axis of revolution to one side of the shell, then to the other).
b. Adjust the ‘Height’ of the tube.
4. Continue to add tubes until the number of tubes equals the number of shells.
5. Now adjust the tubes to lie at the correct height (by adjusting the y-coordinate).
6. Connecting the cylindrical shells
a. First, save a separate file of the cylinders while they are still separate
objects in case you need to go back and change things.
b. Select all of the objects.
c. Make them editable (into polygons) by clicking on the button with the two
spheres and arrow on the far left of the Cinema 4D screen underneath the
undo button.
d. With all the objects still selected under the ‘Mesh’ menu at the top left of
the screen go to ‘Conversion’ and select ‘Connect Objects + Delete’.
8. At the top left of the screen go to File  Export  .STL (*.stl)
9. Save your .stl file, which is now ready to print .
Trouble-shooting
Usually the method indicated above will create a printable object. Sometimes the
interior walls will show, and some printer’s slicers don’t like this. An alternative is
to Boole the cylinders together. This will delete the interior walls of the object. For
instructions on how to use the Boole tool, check out the Instructions on putting
equations on solids. Note that the Boole tool automatically assumes you want 𝐴\𝐵,
you’ll need to select the option 𝐴 ∪ 𝐵 instead.
Ryan McDonnell (‘17)
Elizabeth Denne
Mathematics Department
Washington &amp; Lee University
```