Surface Area vs. Volume

Standard

This demo can really help students see what happens when you change the dimensions of a cylinder, while maintaining the surface area. It appeared in my blog in this form originally. The idea came from Mary Frank, who attended one of my sessions, and stars in the video. It’s similar to Dan Meyer’s Popcorn Picker, but I really like the payoff in Act III. Presented in Dan’s three act format, here are the materials.

Act I – Video

Act II – Information

Have the students make predictions about whether the wider cylinder will overflow, fill right up, or have space left in it. If they want to run calculations, the tubes are simply 8.5 x 11 pieces of overhead paper. One is rolled vertically, and the other is rolled horizontally.

Act III – The Answer

Sequels

  • How tall would the skinnier cylinder have to be to completely fill the wider one?
  • By what factor are the volumes different? Why?
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