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