The most difficult to visualize volumes are the ones that are NOT the result of a revolution around a line. For example… imagine a solid with a circular base, and cross sections that are equilateral triangles with their bases in the circle base. Got it? Now draw it on the board (ha ha … that’s a little math teacher humor – we all should have taken art in college).
Now enter the Wolfram Demonstration “Solids of Known Cross Sections” Throw in a voiceover, a little Camtasia magic, a picture of the Sydney Opera House, and voila! (Check it out here – it’s under a minute) That was MUCH better than drawing it by hand (although all the students did that on the whiteboards for practice).
There is also a WD called “Solids of Revolution” that you might want to check out for this topic.
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