Author:
William Allred, Carrie Robledo
Subject:
Mathematics
Material Type:
Activity/Lab
Level:
High School
Tags:
  • 3D Modeling
  • 3D Printer
  • AP Calculus
    License:
    Creative Commons Attribution Non-Commercial Share Alike
    Language:
    English

    Education Standards

    Calculus AB: Use Basic Equations to Determine the Volume of a Solid (Cylinder)

    Calculus AB: Use Basic Equations to Determine the Volume of a Solid (Cylinder)

    Overview

    Student will be able to use integration and differentiation to determine the volume of a solid and see the connection to the formula of a cylinder.

    Instructor Directions

    Engineering Design Process

    Project Description

    Name of ProjectUse Basic Equations to Determine the Volume of a Solid (Cylinder)
    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 / ActivatorWhat shape would be created when you rotate a rectangle around a given axis?  What equations and constraints would allow you to determine the volume of a rectangle rotated around the x-axis?
    Project SummaryStudent will be able to use integration and differentiation to determine the volume of a solid and see the connection to the formula of a cylinder.
    Estimated Time20-30 minutes
    Materials / Resources (including link to slideshow if available)Graph PaperColored PencilsCalculator3-D Printer
    Tags 

    Project Outline 

    AskWhat would be the volume of rectangle rotated around a fixed line?
    ImagineWhat shape would be created when we rotate a rectangle around a fixed line?
    PlanDraw a model of the imagined figure and determine how to find its volume.
    CreateCreate a model of the figure using graph paper and the equation(s) to find the volume.
    Improve 
    Closure / Student ReflectionsConnect the formula of a cylinder to the equation(s) you used to determine the volume.
    Possible Modifications / ExtensionsUse a 3-D software program to create the solid being discussed.

    Evaluation (Pre/Post)  

    Insert Links to Google Forms

     

    Pretest Link: Evaluating Definite Integrals

    https://docs.google.com/forms/d/10m3eZXuK1NkCGYrT6U3b98uOdb2mFDMK3WCR3hliY9E/viewform?edit_requested=true

    Post-test Link: Using and Applying

    https://docs.google.com/forms/d/e/1FAIpQLSdE3jQF3Ca0FArs6XuDrCZi5udJ1SkTXZtxvcWSvTga0v28OQ/viewform?usp=sf_link

     

    Credits or Modified From

    Additional Resources / Help for teaching this lesson

    Students graph y=0

                        y=3

                        x=0

                        x=4   this will create the rectangle

    Rotate the rectangle around the x-axis.  

    Have students discuss the resulting solids shape.

    Determine the integral and constraints needed and evaluate the volume of the resulting solid.  

    Discuss the relationship of the integrated results and the formula for volume of a cylinder.

    Sample Pictures / Video

     

      
      

     

     

    Teacher Comments of what worked / did not work well

    Creative Commons