Education Technology

Optimisation

Published on 07/22/2005

Activity Overview

This activity will illustrate how geometric problems like finding the minimum/maximum area and volume of a geometric figure can be calculated using the Computer Algebra System CAS tool.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 2 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Write the formula for computing the volume of the cylinder in terms of height and radius of base
  • Solve this equation manually in terms of height
  • Write the formula for finding the surface area of the cylinder
  • Substitute the value of the height [in terms of radius] into the formula for area
  • Study the Area formula in terms of radius and find its derivative
  • Equate the derivative to zero and solve for the radius
  • Calculate the corresponding value of height and compare the numerical values of radius and height
  • Form a conjecture and prove it
  • Repeat the procedure using CAS and understand the advantage of using the tool
  • Identify that the minimum area is obtained when the height is equal to twice the radius


  • Cut a circular piece of paper and fold it to make a cone
  • Determine the height and radius of the cone in terms of the fraction of the paper and the radius of the paper
  • Find the volume in terms of the fraction of the paper and the radius of the paper
  • Determine the derivative and equate it to zero
  • Calculate the fraction of the paper and the corresponding central angle, which give the maximum volume
  • Repeat the procedure using CAS and realize that CAS is superior
  • After the Activity

    Students complete the exercises listed on the activity pages.

    Review student results.

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary