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 = 3.14.A. 19,899.8 square metersB. 4,974.9 square metersC. 9,949.9 square metersD. 6,633.3 square meters

Answer 1

The area of a circle is given by the following formula:

`A=\pi r^2`

Where r is the radius of the circle.

To calculate the area of this circular sector, we can use the following rule of three:

`\begin{gathered} \text{central angle}\to\text{ area} \\ 360\degree\to\pi r^2 \\ 135\degree\to x \end{gathered}`

From this rule of three, we can write the following proportion and solve for x:

`\begin{gathered} (360)/(135)=(\pi r^2)/(x) \\ x\cdot360=\pi r^2\cdot135 \\ x=\pi r^2\cdot(135)/(360) \\ x=3.14\cdot65^2\cdot(135)/(360) \\ x=4974.9 \end{gathered}`

Therefore the correct option is B.