Question

a motion sensor has a range of 65 meters as shown. the ultrasonic waves sweeping out from the sensor span an angle of 135°. what is the approximate area that is within range of the motion sensor? use the value π = 3.14. a. 9,949.9 square meters b. 19,899.8 square meters c. 4,974.9 square meters d. 6,633.3 square meters

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle and \(r\) is the radius.

Step2: Substitute the given values into the formula

Here, \(\theta = 135^{\circ}\), \(r = 65\) meters, and \(\pi=3.14\).

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Answer:

C. 4,974.9 square meters