Surface of Revolution using Tinkercad

Contributed by
Kristen R. Schreck

Multivariable Calculus

Download a PDF of this lesson.


This project introduces students to the design component of

3D printing.  Students will use Tinkercad, a web-based 3D design and modeling tool, to create a unique surface of revolution made up of at least three geometric shapes.  In addition, a name or identifying equation of the surface will be imprinted on the final 3D printed object.


  1. Each student will design his or her own surface of revolution.Students will create a Tinkercad account before coming to class and are encouraged to explore the tutorials provided under the Learn menu on the Tinkercad site before arriving to class on the day of the project.
  2. This project will rely on the student’s prerequisite math knowledge and skills from Calculus II in finding volumes and generating surfaces by revolving a (piecewise) curve about an axis. Students may use any Calculus resource materials to help generate ideas for the type of surface they would like to model.  Students may also find inspiration from familiar objects that can be thought of in a new way – as a surface of revolution.
  3. At least three geometric objects should be used and an identifying name or equation should be imprinted on the final surface.  Students may find the Tinkercad Shape Generators useful in designing their model, along with using the other available geometric shapes and letters.  Gaining familiarity with the techniques of creating holes and grouping shapes will be key in modeling their chosen object.
  4. After successfully completing the design and 3D printing their surface of revolution, students may use Tinkercad to begin a new project and create, then print, an object of their choosing. Or, students may investigate how to download an existing model for 3D printing. The Ultimaker Education website has an extensive compendium of where to find models.


  1. Students will need:

    • to bring a laptop to class on the day of the project to access Tinkercad
    • to install the Cura software on their computer. We will be using the Ultimaker 2+ 3D printer.  Cura is slicing software the printer uses.
    • an SD card (if you already have one please bring it to class – if not, no need to purchase one)

  2. Instructor will need:

    • 3D printer and filament
    • SD card
    • Toolbox

Instructions for Printing:

  1. In Tinkercad:

    • Go to Design:  Properties, to (Re)Name using file format: YourName_3DProj1_color, Set your Public Access, and Save your changes
    • Go to Design:  choose Download for 3D Printing
    • Click on the STL button (a popular format widely used in 3D printing)
    • Save your file to an SD card (or to the desktop, then email the instructor your file)

  2. Open Cura:

    • Go to File: Open File and choose your STL file
    • In the setting palette under Profile:  choose Fast Print
    • Under Platform Adhesion:  choose Brim or Raft
    • Under Support:  Enable Support, if necessary
    • In View Mode:  choose Layers (Cura will calculate the number of layers and printing time)
    • Click on the object (you will see the xyz-frame) and select Scale to resize your object (if desired)
    • Choose Layers again and check printing time
    • Save your file to the SD card (the file will be automatically saved as a G-code file (which gives a list of instructions that the 3D printer understands to print the object)

  3. Go to the Ultimaker 2+ Printer:

    • Insert the SD card
    • Choose Material for the filament type (PLA)
    • Choose Print and select the file to be printed
    • Prepare to be amazed!
    • [Note:  Be very careful!  The printer will take some time to heat up. The nozzle will reach temperatures over 200°C and the build plate will be hotter than 100°C. Do not touch the nozzle or the build plate at any time during the printing process.

Final Product:

  1. The printed 3D object
  2. Photos and/or video of various stages of the object being designed, printed, and supports being removed (if applicable) - take screenshots in Tinkercad, in Cura if supports are used, and of your final object


  3. Photos and/or video of the student with his/her 3D surface of revolution – include a visual scenario which shows how the object might be used


  4. Create a 2D drawing of the (piecewise) curves/shapes that were revolved about an axis to create the surface of revolution


  5. Write a brief account (two paragraphs) of this experience with 3D design and printing.
  6. If your surface meets all the criteria for this project, the instructor will post a photo of your object on YouMagine - in this case you will be required to write a short description of your object and how you created it

Grading Criteria:

CriteriaInstructor Comments Based on CriteriaPoints Earned
Successfully printed 3D surface of revolution
Included photos/video of various stages of object being designed and printed
Included photos/video of students with final product and how the object might be used
Provided 2D graph or drawing of curves that were revolved about an axis to create the surface of revolution
Two written paragraphs describing experience with 3D design and printing