Due Thursday, March 24

50 Points

Individual or pairs

Make a physical model of a solid with a known cross section on a base with a standard function(s).

Guidelines:

• The base function(s) can be any non-linear function except a parabola, square root or absolute value.  If using more than 1 function for the base, the second function can be any of your choice.

• The cross section can be any shape except a square.  If using multiple cross sections, due to more than one region acting as the base of the solid, then the second cross section can be any of your choice.

• The materials used can be no thicker than 0.25".  Your model must be at least 6 inches long and have a minimum of 24 laminations (cross sections).

Presentation must include the following items:

• A clear description of function(s) used.

• Explanation/sample of what the cross section looks like.

• Computed volume for each slice.

• Total volume using a Riemann Sum.

• Theoretical volume as defined by a definite integral.  If your problem is not integrable, you may use the Numerical Integration feature on your calculator.

Scoring:

1. Difficulty of the function and cross section used - 20 points

2. Neatness and appeal of your model - 10 points

3. Presentation of all information and calculations - 20 points

All partner request must be made with both students present by the end of 5th period on Tuesday, March 1.  If no request for a partners is made, it is understood that the student will work on their own.

All work is due on Thursday, March 24, but may be turned in earlier.

Click here for project handout:  Volume Project

Here are some sample pictures. To see the images in a larger window, right-click and select view image.