Question

a water sprinkler sprays water over a distance of 30 feet while rotating through an angle of 130°. what area of lawn receives water? the area of lawn that receives water is □ square feet. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Recall sector area formula

The area of a circular sector is $A = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle, $r$ is the radius.

Step2: Substitute given values

Here, $\theta = 130^\circ$, $r = 30$ ft.
$A = \frac{130^\circ}{360^\circ} \times \pi \times (30)^2$

Step3: Calculate step-by-step

First compute $(30)^2 = 900$, then:
$A = \frac{13}{36} \times \pi \times 900 = 13 \times 25 \times \pi = 325\pi$

Step4: Compute decimal value

$325\pi \approx 325 \times 3.1416 \approx 1021.02$

Answer:

1021.02