4^th Quarter Extra Credit Project

Make a physical model of a "solid of revolution" or "solid built on a base" for classroom demonstration use.

Include for maximum credit (up to -- not automatically -- 10 homework points) ...

• the equation of the function.
• the equation of the line that is the axis of revolution (if a solid of revolution) or boundary of the base (if solid built on a base).
• a "slice" showing the washer, disk, square, or other shape that gets integrated to show the volume.
• the area of the slice.
• the volume of the shape.

The object will be used for classroom demonstration, so it should be something to clearly assist future calculus students to understand these difficult problems. (Too large is as bad as too small.)

Ideas for construction: wood turned on a lathe, pieces of cardboard/foamboard glued together, durable clay, 3-D printing...

Ideas for shapes: problems from section 8.3, problems from the FRQ worksheets from prior AP exams, objects from the solids of revolution page of the National Curve Bank.

Projects are due Monday, January 22, 2018.

Here are some examples: squares on a circle, triangles on a circle (and other shapes...check the different tabs...drag to rotate the shapes)