Rolling+Irrigation+Engineering+Challenge

One type of irrigation system rolls back and forth across a field. The basic design is a bunch of wheels on one axle that rolls the length of the field and reverses direction when it reaches the other side of the field. (A bunch of wheels on one axle can be thought of as a long cylinder.) The goal of this challenge is to design a system where the wheels go a whole number of rotations. This means the circumference of the wheel will be a multiple of the length of the field. For a correctly designed system, a mark on the wheel will start on one edge of the field and stop exactly on the other edge of the field. Also, wheels bigger than small Ferris wheels found at carnivals are not reasonable. This is because the bigger the wheel the more it cost.
 * __ Cylinder Challenge Explained __**

Determine the diameter of the wheels for a rolling irrigation system. The following equation relates distance, wheel circumference and number of rotations. Equation: Distance = Wheel Circumference X Rotations. Distance is the length of the field. The length of the field is 1000 meters. You decide a reasonable number of rotations. Remember the irrigation system must go exactly a whole number of rotations. Also the diameter of the wheel cannot be bigger 24 meters. (Remember that Circumference = 3.14 X Diameter. A model of this system could be made by scaling down the problem by 1000. At this scale 1000 meter would be 1 meter.)

Draw a picture of this challenge.

What is the circumference of a wheel or cylinder that will go exactly 1000m in a whole number of rotations? 1a. Write the equation with the numbers correct.

1b. Solution to the above equation:

……………. = Wheel Circumference

2a. What is the diameter of the cylinder above? Circumference = 3.14(Diameter) Write the equation with the correct numbers:

2b. Solution to the above equation:

…………… = Wheel diameter