# CIRCLES - National 5 Maths

SECTORS sector x A sector is basically a slice. The area of a sector is proportional to the size of the angle at the middle, x. Ex1 sector 90 is quarter of a full turn Sector area = 400cm2 4 = 100cm2 Area = 400cm2 For more difficult angles we can cross-multiply as follows. Ex2 sector Angle 360 =

sector area circ 45 360 = sector 56 45 Area circle = 56m2 360 X sector = 45 X 56 sector = 2520 360 sector = 7m2 Ex3 sector 10cm

108 Angle 360 108 360 = = sector area circ sector 314 r = 10 A = r2 360 X sector = 108 X 314 = 3.14 X 10 X 10 sector = 33912 360

= 314 sector = 94.2cm2 Ex4 15m 144 sector Angle 360 216 360 = = sector area circ sector 706.5 r = 15

360 X sector = 216 X 706.5 A = r2 = 3.14 X 15 X 15 = 706.5 Sector angle = 360 - 144 = 216 sector = 152604 360 sector = 423.9 arc = 424m2 ( 3 sfs) Ex5 18cm 40 A slice of pizza has a radius of 18cm. The angle in the centre is 40. What is its area? *********** r = 18 Angle

= 360 A = r2 40 = = 3.14 X 18 X 18 360 = 1017.36 360 X sector = sector area circ sector 1017.36 40 X 1017.36 sector = 40694.4 360 = 113.04 = 113cm2 Work for this is on pages 41-43, Ex2

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