See the task page.

I set up the problem and then had a whale of a fun time figuring out an answer. I suspect I used a railroad spike where a penny nail would have sufficed, though, so I’d like to see how you’d solve it. Leave your method or a link to a scanned scribble sheet in the comments.

**BTW**: This is another example of the advantages of the digital medium I’m working with. The student sees two images. One looks almost identical to the other.

With the first image, I can ask the student to guess where the water levels falls in the rotated traveler. Then we lay down a mathematical structure on the image and the student works on a more abstract task. But I’ll wager that when people use this task they’ll just print out the second image because, wow, that’s a lot of paper to use for something as fleeting as a guess. That’s an advantage of digital media: students can work on more concrete tasks using more concrete representations, then abstract tasks using more abstract representations. At no extra charge.

**2012 Jun 16**. From Discovering Geometry, Fifth Edition, pg. 548:

A sealed rectangular container 6 cm by 12 cm by 15 cm is sitting on its smallest face. It is filled with water up to 5 cm from the top. How many centimeters from the bottom will the water level reach if the container is placed on its largest face?