First you'll construct a three-dimensional solid out of some cardboard, following the instructions on the study sheet.
Then you'll compute the volume of your solid and answer a few questions about it. This isn't a thought experiment; you really do need to make this model. The point isn't just to learn a formula; it's to get a feeling for solids and volume. The word "feeling" here means real, physical, sense-of-touch, feeling. You're about to enter the three-dimensional world, and you'll need your senses to understand what you're doing.
Finally, you'll post answers to all the following questions:
Describe as best you can what your solid looks like. What cross sections did you use? What familiar solids does it remind you of?
Explain your method for calculating its volume. Would you have computed the same volume if you'd arranged your cross-sections differently? Is that what you'd expect to happen?
Explain your method for calculating its volume. Would you have computed the same volume if you'd arranged your cross-sections differently? Is that what you'd expect to happen?
What did you learn about volume from this experiment?
