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ARCS

ARCS. arc. The length of an arc is proportional to the size of the angle at the middle, x °. x °. Ex1. arc. 90 ° is quarter of a full turn. so arc = 44cm  4 = 11cm. Circumference = 44cm. For more difficult angles we can cross-multiply as follows…. Ex2. arc. Angle = arc.

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ARCS

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  1. ARCS arc The length of an arc is proportional to the size of the angle at the middle, x°. x° Ex1 arc 90° is quarter of a full turn so arc = 44cm  4 = 11cm Circumference = 44cm

  2. For more difficult angles we can cross-multiply as follows…. Ex2 arc Angle = arc 360 circumf 72° 72 = arc 360 45 360 X arc = 72 X 45 Circ = 45m arc = 3240  360 arc = 9m

  3. Ex3 arc Angle = arc 10m 108° 360 circumf 108 = arc 360 62.8 r = 10 so d = 20 360 X arc = 108 X 62.8 C = d arc = 6782.4  360 = 3.14 X 20 = 62.8 arc = 18.84m arc = 18.8m (3 sfs)

  4. Ex4 arc Angle = arc 15m 144° 360 circumf 144 = arc 360 94.2 r = 15 so d = 30 360 X arc = 144 X 94.2 C = d arc = 13564.8  360 = 3.14 X 30 = 94.2 arc = 37.68m arc = 37.7m ( 3 sfs)

  5. Ex5 A slice of pizza has a radius of 18cm. The angle in the centre is 40°. How long is the stuffed crust? 40° 18cm *********** Angle = arc r = 18 so d = 36 360 circumf C = d 40 = arc = 3.14 X 36 360 113.04 = 113.04 360 X arc = 40 X 113.04 arc = 4521.6  360 = 12.56 = 12.6cm

  6. Ex6 The corner pocket on a pool table has a radius of 4cm and a minor angle of 70°. Find the length of the curved padding. 70° 4cm 290° Angle = arc 360 circumf r = 4 so d = 8 290 = arc 360 25.12 C = d 360 X arc = 290 X 25.12 = 3.14 X 8 arc = 7284.8  360 = 25.12 = 20.2355….. Small angle = 70°. = 20.2cm 3sfs Large angle = 290°.

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