Your assignment is to find the volume of a wine fermentation tank made by Sonoma Stone. When converted to the metric system (because wine bottles have a volume of 750 milliliters), the boundary of the central cross section of the interior of the tank is very nearly All distances are measured in centimeters. In other words, the interior of the tank is interior of the surface described by rotating that curve about the axis. The volume of that region can be found as an integral. I.e. we are evaluating an integral to find the volume of a surface of rotation. For the real tank, .
- Create a Maple document (or a Maple command file, if you prefer) to evaluate the volume for any value of between 0 and 0.02. Comment the document liberally.
- Use the implicitplot and implicitplot3d commands to plot both the cross section of the tank, and a 3-d view of the interior of the tank, when .
- Plot the value of the volume of the tank for values of between 0 and 0.02.
- Write a LaTeX document describing how to find the volume of the tank. Remember that this is a mathematical discussion - you will use mathematical notation to describe the process - not computer or Maple notation. Moreover, the instructor has no interest in a description of the computational steps in finding the volume - he wants to know how you solved mathematically for the various components of the integral. Obviously, your document will include some astute observations about the way that the volume depends on , and so on.
- Make sure to tell how many bottles of wine one expects to get out of the tank when . Do not try to include the solution for all values of , unless it were in an appendix.
- Make sure to include the pictures of the cross-section and 3-d view of the tank that you created, as well as the one for variation of volume with .
This assignment is worth 60 points and is due at 3:00 on Friday, 7 December (a day that will live in infamy). It is turned in when a message containing three attachments appears in the instructor's email inbox. The attachments are a) the Maple .mw file (or if you did a .mc file, send that); b) the .tex file; and c) the .pdf file you created from the LaTeX .
Welcome to Math 300 for summer, 2013.