# Sprinkler System Design

After determining how to write the equations of circles through the Shell Center activity: Equations of Circles 1, my students needed to practice using equations of circles. I decided to find my high school on Google Maps and make a screenshot. I then imported the screenshot into Desmos and adjusted the size of the image so that 1 unit = 1 foot in my image. I shared the link using google classroom, but it could be shared in any way that you choose.

The assignment was to design a sprinkler system that covered all of the grass, at a minimum cost. I researched commercial sprinkler systems and found that the maximum radius of a sprinkler is 15 feet. Here are some students designs (click on the image to go to Desmos):

Next year I want to provide students with a list of pricing per foot for trenching, sprinkler pipe, heads for various radii, control box and also require that they calculate the cost for their design. I also want to require that they draw in the underground piping which would allow students an opportunity to review linear equations and piece wise functions as well. Additionally, calculating costs would force students to apply distance to find lengths between the sprinkler heads too.

[update 7/10: Desmos made a formula to calculate pipe length! I could have students explain what this formula does. click on the image to go to Desmos.]