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Volume Elements

Creation's quality: 5.0/5 (1 vote)
Evaluation of members on the printability, utility, level of detail, etc.
  • 1 like
  • 1 download

3D model description

These models are useful when discussing different coordinate systems. In my Multivariable Calculus course we learn about rectangular, cylindrical, and spherical coordinates. Each model represents a "chunk" of space as it would be naturally cut using the corresponding coordinate system. In particular, these are useful when discussing triple integrals.

I enjoy passing these around class and having the students get a hands-on feel for each element of volume and understanding ΔxΔyΔz (rectangular) vs. ΔzΔrΔΘ (cylindrical) vs. ΔρΔΘΔφ (spherical).

Created in Mathematica.

Also see my Ring Sector Model.

3D printing settings

Note that when I import the models into Simplify3D they look incomplete or empty. However, Simplify3D sliced them perfectly.

Approximate model sizes:
Rectangular 50 x 50 x 50 mm
Cylindrical 65 x 71 x 50 mm
Spherical 63 x 57 x 61 mm

  • 3D file format: STL
  • Last update: 2021/03/12 at 05:51
  • Publication date: 2019/11/16 at 23:24



Designs 130
Downloads 2k
Sales US$486
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I am a high school math teacher and 3D printing hobbyist. I have been 3D printing since 2017 and enjoy making things for my classes and my own children and home in San Diego, California, USA.

I have a 3D printing sub-site See my video on YouTube and my user story written and published by Simplify3D. I design with Mathematica, CorelDRAW, Fusion 360, and Tinkercad. I love my MakerGear M3-ID and my Palette 2S Pro. I have a Monoprice Mini as well.



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