8.2 Length of an Arc of a Circle

(A) Formulae for Length and Area of a Circle


r = radius    A= area    s = arc length    q = angle    l = length of chord


(B) Length of an Arc of a Circle



Example 1:
An arc, AB, of a circle of radius 5 cm subtends an angle of 1.5 radians at the centre.  Find the length of the arc AB.

Solution: 
s = rθ
Length of the arc AB = (5)(1.5) = 7.5 cm



Example 2:
An arc, PQ, of a circle of radius 12 cm subtends an angle of 30° at the centre.  Find the length of the arc PQ. 

Solution: 
Length of the arc PQ
= 12 × 30 × π 180 = 6.283  cm



Example 3:
In the above diagram, find
(i) length of the minor arc AB
(ii) length of the major arc APB

Solution: 
(i) length of the minor arc AB = rθ
= (7)(0.354)
= 2.478 cm

(ii) Since 360o = 2π radians, the reflex angle AOB
= (2π – 0.354) radians.

Length of the major arc APB
= 7 × (2π – 0.354)
= 7 × [(2)(3.1416) – 0.354]
= 7 × 5.9292
= 41.5044 cm

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