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Rolling Tires/Stacking Pipes

You have two activities to explore today.  Answer all the questions on a separate sheet of paper.
Rolling Tires:
Watch the video below.

Rolling Tires Act 1

Q1: Estimate how rotations will the BIG tire make before hitting/missing the target? How many rotations will the small tire make before hitting/missing the target?

Q2: Make a prediction for each tire whether it will hit the target or not.

Watch the next video to help you calculate the answer to the above questions.

Rolling Tires Act 2

Using the information from the previous video, answer the following questions.  Show your work!
Q3: How many rotations did the BIG and small tires make to reach the target? Be as exact as possible.

Watch the final video to see if your answers were correct.  If they were incorrect, do the correct work below question 3.

Rolling Tires Act 3

Stacking Pipes:
Pipes can be stacked in various ways.  Pictured below are two ways staggered and non-staggered.  This activity will look at height difference of these two methods.

Our task will be to find the height difference after 20 layers of pipe.  The first few layers are pictured in the video below.

Stacking Pipes Act 1

The pictures below show the pipe's diameter is 5.6 centimeters.

Q4: What is the height difference after 20 rows of pipe?
Use the diagram below to begin solving this problem.  It may be helpful to find the height at different stages.  Also, can you find a general formula using r for radius to give the height at any stage?          Show your work!


The video below gives the answer to this problem.  The picture below gives a closeup of the answer.

Stacking Pipes Act 3

h ≈ 14.255 cm