In the diagram O is the center of circle PRQ. The radius is 3.5cm and ?POQ = 50o. Use the diagram to answer question below. (take ? = 3.142) Calculate, corr...

In the diagram O is the center of circle PRQ. The radius is 3.5cm and ?POQ = 50^o. Use the diagram to answer question below. (take ? = 3.142)
Calculate, correct to three significant figures, the area of sector OPQ

Answer Details

The area of sector OPQ is a fraction of the area of the whole circle. The whole circle has an area of πr², where r is the radius. In this case, r = 3.5 cm, so the area of the whole circle is: A = π(3.5 cm)² = 38.465 cm² The sector OPQ makes up a fraction of the whole circle. The fraction is equal to the central angle of the sector divided by 360 degrees. In this case, the central angle is 50 degrees, so the fraction is: 50/360 = 5/36 So the area of sector OPQ is: A = (5/36)×38.465 cm² ≈ 5.350 cm² Therefore, the correct option is (b) 5.350cm².