SECTORS A sector is basically a “slice”. x° The area of a sector is proportional to the size of the angle at the middle, x°. Ex1 90° is quarter of a full turn sector Sector area = 400cm2  4 = 100cm2 Area = 400cm2

For more difficult angles we can cross-multiply as follows…. Ex2 Angle = sector sector 360 area circ 45° 45 = sector 360 56 360 X sector = 45 X 56 Area circle = 56m2 sector = 2520  360 sector = 7m2

Ex3 Angle = sector 360 area circ 108 = sector 360 314 10cm 108° 360 area circ 108 = sector 360 314 r = 10 360 X sector = 108 X 314 A = r2 sector = 33912  360 = 3.14 X 10 X 10 = 314 sector = 94.2cm2

Ex4 Angle = sector 360 area circ 216 = sector 360 706.5 15m Angle = sector 144° 360 area circ sector 216 = sector 360 706.5 r = 15 360 X sector = 216 X 706.5 A = r2 sector = 152604  360 = 3.14 X 15 X 15 sector = 423.9 = 706.5 arc = 424m2 ( 3 sfs) Sector angle = 360° - 144° = 216°

Ex5 A slice of pizza has a radius of 18cm. The angle in the centre is 40°. What is its area? 40° 18cm *********** r = 18 Angle = sector 360 area circ A = r2 40 = sector = 3.14 X 18 X 18 360 1017.36 = 1017.36 360 X sector = 40 X 1017.36 sector = 40694.4  360 = 113.04 = 113cm2

Work for this is on pages 41-43, Ex2