08 Dec Landscape Irrigation: Circles Upon Circles

Posted at 01:24h in Math Problems by
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Goal: Position 3 sprinkler heads in a 12 feet by 18 feet rectangular lawn to optimize water coverage but to minimize water waste. Watering an area twice is considered waste but watering the street or non-lawn areas is worse. The sprinkler heads are manufactured for a 6 foot spray radius. The heads can be set as full circle, half circle, or quarter circle spray pattern.

IrrigationProcedure

  1. Work as a group on this activity for the first 3 steps. You may want to work with another group to physically model this problem as suggested in step 2.
  2. Use a tape measure to mark the corners of the lawn (12’x18’) in a parking lot with sidewalk chalk (or painters tape if in the cafeteria). Each “lawn” will need 3 pieces of 6 foot string that models the spray radius for you to experiment with sprinkler head locations. One student holds the end of the string on the sprinkler head location and another moves the string to illustrate water coverage. Move the sprinkler heads around the lawn to determine the best locations for the 3 sprinklers.
  3. Instead of step 2, you can do the problem to scale (1”=1’) on a piece of graph/grid paper with a compass and a ruler if your teacher allows.
  4. Once you have determined where to locate the 3 sprinkler heads and the spray pattern type, full circle, half circle, or quarter circle spray pattern, you will need to draw a scale drawing (1” = 1’)of your solution. Please do this on graph/grid paper supplied by your teacher.
  5. Answer the following questions. You are allowed to estimate area from the scale drawing of any region that you have not learned how to calculate area for.
  • How much of the lawn area is receiving water?
  • How much of the area is not watered?
  • How much area is watered twice or more?
  • How much area is being watered outside of the 12’ X 18’ lawn?
  • How does your answer compare to other groups?
  1. If you could order any number of 6’ spay radius sprinkler heads, and they could be set to either full circle, half circle, or quarter circle spray, where would you position them and what spray pattern would you choose? Answer the questions to #5 with your new arrangement.
  2. What are the pros/cons of your design in #6 when compared to your first design in #4?

Extension: Write the equations of the circles/partial circles covered by the sprinkler heads.