Answer:
37% of the backyard will not be covered by the water from the sprinkler.
Step-by-step explanation:
The sprinkler is at the centre (0,0). It squirts in a circular motion. The other end of the radius is at (12,16).
First we will calculate the radius of the circle.
[tex]r = \sqrt{(12-0)^2 + (16-0)^2}\\r = \sqrt{144 + 256}\\r = \sqrt{400}\\r = 20[/tex]
Area of the circle = πr^2
= 3.1416*(20)^2
= 3.1416*400
= 1256.64
Area of yard = 40 ft * 50 ft
= 2000
Percent covered by the water = 100*(area of circle/area of yard)
= 100*(1256.64/2000)
= 100*(0.628)
= 62.8%
= 63%
Area not covered by the water = 100 - 63
= 37%
