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Volume Elements

Volume-Elements.jpg Volume Elements
Volume Element Rectangular.stl Volume Elements
Volume Element Cylindrical.stl Volume Elements
Volume Element Spherical.stl Volume Elements
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Creation quality: 5.0/5 (2 votes)
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  • Volume Element Cylindrical.stl
  • Volume Element Rectangular.stl
  • Volume Element Spherical.stl

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Last update 2021-03-12 at 05:51
Publication date 2019-11-16 at 22:24
Design number 85615
abbymath

abbymath

3D printer file info

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 Ξ”xΞ”yΞ”z (rectangular) vs. Ξ”zΞ”rΞ”Ξ˜ (cylindrical) vs. Ξ”ΟΞ”Ξ˜Ξ”Ο† (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

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