Question

A rotating sprinkler can spray out to 12 feet. The sprinkler rotates through an angle of 200 degrees . How many square feet of grass is watered by the sprinkler ( sector area )

Answer 1

Given:

The range of spray is 12 feet and rotation angle is 200 degree.

Required:

How many square feet of grass is watered by the sprinkler.

Explanation:

Here

radius r = 12 ft

angle of rotation = 200 degree

We have a formula to find the sector area

$A=\frac{\pi r^2\emptyset}{360}$

now put the value

$A=\frac{3.14*12^2*200}{360}$$A=\frac{3.14*144*20}{36}$$A=\frac{3.14*144*10}{18}$$A=\frac{3.14*144*5}{9}$$A=3.14*16*5$$A=251\text{ ft}^2$

Final Answer:

251 square feet of grass is watered by the