Question

Sally bought a sprinkler that squirts in a circular direction. With the center of the sprinkler as the center, it sends out water far enough to reach a point located at (12,16). If Sally's backyard is 40 feet long by 50 feet wide, about what percent of the backyard will NOT be watered directly? (Hint: Find area of circle and divide by area of yard to determine the percent that IS covered by the water)

Answer 1

37% of the backyard will not be covered by the water from the sprinkler.

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.

`r = √((12-0)^2 + (16-0)^2)\\r = √(144 + 256)\\r = √(400)\\r = 20`

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%