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.

Dr. Maria Andersen has spent most of her career teaching, writing curriculum, and developing digital products for learning. Recently she returned to the classroom, having new teaching adventures in K-12 middle and high school.