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