Page 88 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

(a) The length of the minor arc PQ, l = 2 πr􏰀 􏰄
22 360 60 = 2 􏰀 7 􏰀 5.6 cm 􏰀360
= 2 􏰀 22 􏰀 0.8 cm 􏰀 60 = 22 􏰀 0.8 􏰀 13 cm 360
= 5.87 cm (correct to 3 s.f) (b) The area of the minor sector POQ,
PQ,A=πr2􏰀 􏰄
22 360 60
= 7 􏰀 (5.6 cm)2 􏰀360 1 = 22 􏰀 (5.6 􏰀 5.6 cm2 􏰀 6
71 = 11 􏰀 5.6 􏰀 0.8 􏰀 3
cm
= 16.4 cm2 (correct to 3 s.f)
EXAMPLE 4
Arc A subtends an angle of 60° at the centre of a circle of radius 5.6 cm.
EXERCISE 4.4
Use π as 22 in the following questions. 7
1. An arc subtends an angle of 65° at the centre of a circle of radius 3.9 cm. Calculate
(a) the length of the minor arc (b) the area of the minor sector.
2. An arc of a circle subtends an angle of 53° at its centre. The radius of the circle is
4.7 cm. Find
(a) the length of the minor arc (b) the area of the minor sector.
3. A clock is reading 04: 00h. The radius of the circle forming the face of the clock is 14cm. Calculate
(a) the length of the minor arc defined by the time
(b) the area of the minor sector defined by the time
Calculate: Take 􏰃 = 22
7
L=5.87m
P A=16.4 m Q
(a) the length of the minor arc (b) the area of the minor sector.
L=5.87m
A A=16.4 m Q
00
82
􏰄=60o r=5.6cm
􏰄=60o r=5.6cm