ARCS arc x The length of an arc

ARCS arc x° The length of an arc is proportional to the size of the angle at the middle, x°. Ex 1 arc 90° is quarter of a full turn so arc = 44 cm 4 = 11 cm Circumference = 44 cm

For more difficult angles we can cross-multiply as follows…. Ex 2 arc Angle 360 = arc circumf 72 360 = arc 45 72° Circ = 45 m 360 X arc = 72 X 45 arc = 3240 360 arc = 9 m

Ex 3 arc 10 m 108° r = 10 so d = 20 C = d Angle 360 108 360 = = arc circumf arc 62. 8 360 X arc = 108 X 62. 8 = 3. 14 X 20 arc = 6782. 4 360 = 62. 8 arc = 18. 84 m arc = 18. 8 m (3 sfs)

Ex 4 arc 15 m 144° r = 15 so d = 30 C = d Angle 360 144 360 = = arc circumf arc 94. 2 360 X arc = 144 X 94. 2 = 3. 14 X 30 arc = 13564. 8 360 = 94. 2 arc = 37. 68 m arc = 37. 7 m ( 3 sfs)

Ex 5 18 cm 40° r = 18 so d = 36 C = d = 3. 14 X 36 = 113. 04 A slice of pizza has a radius of 18 cm. The angle in the centre is 40°. How long is the stuffed crust? ****** Angle = arc 360 circumf 40 = arc 360 113. 04 360 X arc = 40 X 113. 04 arc = 4521. 6 360 = 12. 56 = 12. 6 cm

Ex 6 The corner pocket on a pool table has a radius of 4 cm and a minor angle of 70°. Find the length of the curved padding. 70° 290° 4 cm Angle 360 r = 4 so d = 8 C = d = 3. 14 X 8 = 25. 12 Small angle = 70°. Large angle = 290°. 290 360 = = arc circumf arc 25. 12 360 X arc = 290 X 25. 12 arc = 7284. 8 360 = 20. 2355…. . = 20. 2 cm 3 sfs