About
Volumes of Revolutions: The Method of Washers
“Integrate the Cake”
OVERVIEW
For this project, we are going to bring calculus into the kitchen to analyze a classic bakery form known as the bundt cake. Although this familiar dessert may seem innocuous at first glance, upon close inspection geometry is revealed that requires a fairly sophisticated mathematical analysis in determining its volume.
We hope this hands-on project is not only fun but very helpful, especially to the visual learner. As part of the overall project display we intend on awarding pieces of cake to students within the context of a mathematical contest where students must display their mathematical knowledge in solving various problems.
The center piece of this project is the application of integral calculus specifically in the form of volumes of revolutions. First, students must model the parabolic nature that lies within the bundt cake form. Then students will apply the method of washers to slice the cake horizontally into infinitesimal sections, apply integral calculus, and finally revolve the integration 360 degrees to obtain the volume of the cake.
Four students will be involved with this project and each will have a slightly different cake to analyze and compare with their teammates. Furthermore, in addition to completing an open-ended assignment involving the analysis of their cake, each student must: bake a bundt cake, submit a written report on the applications of integral calculus, complete a reflection on their project experience, build a model that represents the washer sections of the cake, contribute to the overall main project display, create a power point presentation, and interact with students from other schools through
video conferences on Tuesday, April 26, 2011
Note: Cooperating schools can analyze any cake form that they choose and apply any form of mathematical analysis in determining the volume of their cake. It is our intent to compare and contrast various shapes and the methods of determining their volumes mathematically.
Please contact Peter Santino for project details, psantino@nps.k12.nj.us
Please click on the link below to register for the program
https://spreadsheets.google.com/viewform?formkey=dGpyOXp0Z3I4bmg5elRscmpRc01ESFE6MA
Timeframe
March 2011 - April 2011
Status
Completed