See the task page.
FWIW, this is exactly the reaction I hoped to provoke with that video:
This is a classic textbook problem that we actually did early in the year (Discovering Geometry, Ch. 10) and at the time I recall a number of students asking me for help. They weren’t entirely sure what the problem was asking, and they didn’t know where to start. I’m sure a large number of my no-homework doers saw a block of text and skipped it entirely. We did this today, and kids totally bought into it.
This was awesome. I just showed my 8 year old and asked, "Which one will hold the most popcorn?" He answered, "Both." I now need to show the other kids.
2012 Jun 16. From Discovering Geometry, Fifth Edition, pg. 548:
If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two longer sides together, you get a tall, thin cylinder. If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two shorter sides together, you get a short, fat cylinder. Which of the two cylinders has the greater volume?