Find the Area of a Sector of a Circle Having $$\theta$$

question 194

Multiple Choice

Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-A sensor light installed on the edge of a home can detect motion for a distance of $44 \mathrm { ft }$ . in front and with a range of motion of $254 ^ { \circ }$ . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

• A) \(8582.55 \mathrm { ft } ^ { 2 }\)
• B) \(4291.18 \mathrm { ft } ^ { 2 }\)
• C) \(8582.65 \mathrm { ft } ^ { 2 }\)
• D) \(4291.28 \mathrm { ft } ^ { 2 }\)