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Diameter or Radius of a Circle Given Circumference

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Credit: USDA
Source: http://commons.wikimedia.org/wiki/File:PivotIrrigationOnCotton.jpg
License: CC BY-NC 3.0

Do you know what irrigation is? Irrigation is a method of bringing water to a large area, usually to water crops. Sometimes this is as simple as a sprinkler system above the ground. Large circles of land can be watered effectively using a more complex system called center-pivot irrigation.

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A center-pivot irrigation system, like the one pictured above, consists of sprinklers set up on pipes that are supported by wheeled towers. When the irrigation system moves, it travels in a circular path. In fact, it moves along the circumference of a circle. The irrigation system forms the radius of the circle, and the watering happens within the area of that circular space.

Credit: Bob Heims/U.S. Army Corps of Engineers
Source: http://commons.wikimedia.org/wiki/File:Center_pivot_irrigation_Idaho.jpg
License: CC BY-NC 3.0

If you look closely at the picture above, you can see the water line of each irrigation system moving along the circumference of a circle. If you know the circumference of a circle, you can figure out its radius. Therefore, knowing the circumference of the area of land that needs to be watered would allow a farmer to choose an irrigation system of the correct length. Based on the circumference, he can choose a system with the best length (radius) for the area!

See for yourself: http://www.youtube.com/watch?v=X0zyqjU9Jlc

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The circumference of the area of land reached by a center-pivot irrigation system is 10,048 feet. Can you figure out the length of the irrigation system?

Image Attributions

  1. [1]^ Credit: USDA; Source: http://commons.wikimedia.org/wiki/File:PivotIrrigationOnCotton.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Bob Heims/U.S. Army Corps of Engineers; Source: http://commons.wikimedia.org/wiki/File:Center_pivot_irrigation_Idaho.jpg; License: CC BY-NC 3.0

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