Setting Up Sprinklers Task Assessment
Geometric Standards
G-C.A: Understand and apply theorems about circles
G-C.B: Find arc lengths and areas of sectors of circles
Selina has a 9 meter by 12 meter lawn that she wants to water. She has two sprinklers; each of the sprinklers can water grass within a 6-meter radius. Selina wants to set up the two sprinklers so that they are on corners of the lawn. She would like for the sprinklers to water as much of the lawn as possible because she will have to manually water the part of the lawn that is not covered by the sprinklers.
Selina considers two different scenarios for placing the sprinklers. One scenario is to put the sprinklers at adjacent ends of a 12-meter side of the lawn (black point is a sprinkler). The other is to put the sprinklers at opposite corners of the lawn. (See the figures in the applet below.)
1. Which sprinkler placement covers the largest amount of grass? Justify your answer using the applet above and show your calculations.
2. If Selina could place the sprinklers anywhere on the lawn or around the perimeter, use at least one way to show where she would have to place the two sprinklers so that the largest area of grass is covered. Justify your answer using the applet below and show your calculations.