Question

16
Select the correct answer.
A rotating sprinkler head sprays water as far as 20 feet. The head is set to cover a central angle of 80 degrees. What area of grass will be watered?
A. 200/9 pi ft^2
B. 800/9 pi ft^2
C. 80/9 pi ft^2
D. 760/9 pi ft^2

Answer 1

Using the area of a circle, it is found that the area of the grass that will be watered is given by:

B. 800/9 pi ft^2

What is the area of a circle?

The area of a circle of radius r is given by:

$A = \pi r^2$.

In this problem, a rotating sprinkler head sprays water as far as 20 feet, hence the radius is of r = 20 ft.

It covers a central angle of 80º, while an entire circle has 360º, hence the area of grass that will be watered corresponds to 80/360 = 2/9 of the area of the circle.

Hence the watered area in ft² is given by:

$A = \frac{2}{9}\pi (20)^2 = \frac{800\pi}{9}$

Which means that option B is correct.

More can be learned about the area of a circle at https://brainly.com/question/17326298