This worksheet is designed to replace a lecture on finding the maximum volume of a cylindrical cup formed from a circular piece of paper.
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 wrinkle it over the top of a metal can, so they can see how I'm forming the cylindrical cup.
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