A sprinkler on a golf green is set to spray water over a distance of 12 meters and to rotate through an angle of 130°.Find the area of the region.Round your answer to two decimal places.

Question

A sprinkler on a golf green is set to spray water over a distance of 12 meters and to rotate through an angle of 130°.Find the area of the region.Round your answer to two decimal places. ​

Quizplus · Accepted Answer

The area covered by the sprinkler can be calculated using the formula for the area of a sector of a circle, $A = \frac{1}{2}r^2\theta$, where $r$ is the radius (12 meters in this case) and $\theta$ is the angle in radians. First, convert 130° to radians: $130° \times \frac{\pi}{180°} = \frac{13\pi}{18}$. Then, plug the values into the formula: $A = \frac{1}{2} \times 12^2 \times \frac{13\pi}{18} \approx 163.36$ square meters.

A Sprinkler on a Golf Green Is Set to Spray