This worksheet is designed to replace a lecture on finding the maximum volume of a cylindrical cup formed from a circular piece of paper. In this case, no paper is wasted in "wrinkling," as occurred in the previous activity.
I start out class with a 15-minute "mini-lesson," giving my students some basic examples of what today's lesson will be about: I start with a circular sheet of paper, and then I show them how I want to transform it into a smooth cylinder. We accept that we can reshape a given area in the shape of a "washer" into a rectangle with the same area, as that process is not possible with paper.
Once the mini-lesson is over, I have them get to work within their groups on this worksheet, and I circulate to make sure they are getting the purpose of the questions.
Students are expected to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.
Keywords: calculus, optimization, maximum volume, Jonnard