Problem Solving for CGS Geometry Students

Six problems are outlined below. One problem must be handed in to your math teacher. A grading rubric will be used to score your solution. Please consult this rubric to ensure you are handing in a complete and thoughtful solution. The honor code is to be followed in completing this assignment. Here are the problems to choose from:

#1 I have an unusual dog run in my yard. A fifty-foot rope is tied at each end to two pegs that are fourteen feet apart. My dog is tethered to the rope, but the tether is loose and slides freely along the rope between the pegs. I lay treebark over the area of my yard that the dog can reach. What is the area of the region that the dog can reach?

#2 In the country of Puevigi, the population consists of Soothsayers, who never lie, Dissemblers, who always lie, and Diplomats, who alternately lie and tell the truth. If you meet a citizen of Puevigi, how with just two questions can you determine to which group he belongs?

#3 All Tied Up

I really enjoy wrapping presents - pieces of ribbon, bows and pretty paper - trying to make the present as attractive as possible. A picutre of the box with the ribbon touching all six faces.

I like to run a ribbon around the box so that it makes a complete loop with two parallel pieces of ribbon on the top (and on the bottom) of the box.

The ribbon crosses every face once, except the top and bottom, which it crosses twice.

The ribbon rests tightly against the box all the way round because the angle at which it meets a corner is continued onto the next face.

I can cut the ribbon in advance of placing it around the box and I can slide the ribbon around a little to position it.

If the box is 20 cm by 10cm by 5cm - how long will the ribbon be?

Show why it is possible for me to "slide" the ribbon.

What will it be for any box with height h, width w and length l? (n.b. the length and width are the longer distances and form the top of the box. Would the string be longer or shorter if this was not the case?)

#4 Two cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, how many units are in the length of the radius of the wider can? Express your answer in simplest radical form.

#5 Heeding the advice to "Go West, young man," Harold and Horace Greedy set out for Las Vegas to make their fortunes. Luck was with the Greedy brothers, for each doubled his money every h our. Harold, who began with $20, gambled for 20 hours and then sent his fortune home. The next day, Horace began with $40 and gambled until his fortune matched his brother's. For how many hours did Horace Greedy gamble that day?