William Allred, Carrie Robledo
Material Type:
High School
  • 3D Modeling
  • 3D Printing
  • AP Calculus
    Creative Commons Attribution Non-Commercial Share Alike

    Education Standards

    9-12 Calculus: Volume: Cross Sections

    9-12 Calculus:  Volume: Cross Sections


    Create a 3 dimensional model using known base shapes such as square or rectangle, circle or semi-circle

    Instructor Directions

    Engineering Design Process

    Project Description

    Name of ProjectVolume: Cross Sections
    Subject AreaAP Calculus AB
    Targeted StandardsEU 3.4 The definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulation.  LO 3.4D Apply definite integrals to problems involving area, volume.
    Driving Question / Problem / ActivatorHow do we find volume using Known Cross Sections with a variety of bases?
    Project SummaryCreate a 3 dimensional model using known base shapes such as square or rectangle, circle or semi-circle
    Estimated Time60-90 minutes
    Materials / Resources (including link to slideshow if available)Paper, graph paper, graphing calculator, colored pencils, 3 D printer with filament

    Project Outline 

    AskHow can a seemingly 2 D shape have volume
    ImagineUsing perspective:  imagine the underside of the surface of a lake with depth related to the dimensions of the 2 D visible shape
    PlanShow students a seemingly 2 D figure; apply area between 2 curves to model the figure’s depth
    CreateStudents will first create an area between 2 curves and choose/select a cross section.  They will model their 3 D shape using graph paper and create a tangible model using the 3 D printer
    Closure / Student Reflections 
    Possible Modifications / Extensions 

    Evaluation (Pre/Post)  

    Insert Links to Google Forms


    Pretest Link:


    Post-test Link:



    Credits or Modified From



    Additional Resources / Help for teaching this lesson




    Sample Pictures / Video





    Teacher Comments of what worked / did not work well

    Creative Commons