13.18 Chapter 13
Consider the sectors below with r as their radii.
P
Q
rO
x
P
Q'
rO
y
P
Q''
rO
z
We note that when the angle of a sector increases, the area of the sector
also increases.
In fact, the area of a sector and its angle are proportional. They have the
following relationship:
Area of a sector
Area of a circle = angle of the sector
360c
Therefore, for a circle of radius r, if the angle of a sector is i,
then
area of the sector
rr2 = 360c
i
i.e.
Area of a sector = 360c
i # rr2
O r
ri
Quick
Example (a) Area of the sector in the figure
= 360
80 c
c # r # 102 cm2
= .cm69 8
2, cor. to 3 sig. fig.
(b) In the figure,
reflex +AOB = 360c - 80c
= 280c
Area of the sector
= 360
280
c
c # r # 202 m2
= m977
2, cor. to 3 sig. fig.
Area of a circle = rr2
◀
10 cm
80°
Quick Quiz
Find the area of the sector
in each of the following
figures, correct to 1 decimal
place.
(a)
5 cm
110°
(b)
225°
8 mm
80°
20 m
A
O
B
Mensuration (II) 13.19
The area of the sector in the figure is 24r cm2.
Find the radius of the sector.
Let r cm be the radius of the sector.
a Area of the sector = 24r cm2
`
360
60 c
c # r # r2 = 24r
r2 = 144
r = 12
` The radius of the sector is 12 cm.
60°
Level 1
Example 9
Solution
The area of the sector in the figure is 27r cm2.
Find the radius of the sector.
9
Instant Drill
➥ Ex 13B 11, 13
30°
In the figure, the radius and the area of the sector OPRQ
are 6 m and 32r m2 respectively. Find the length of PRQ
(,
correct to the nearest 0.1 m.
O
6 m
P
Q
R
Level 1
Example 10
6
2 連環學習組合 (Learning Combo)
Book 2B Ch.13•P.13.18-13.19
重要概念 簡例 + 試算
Quick Example + Quick Quiz
例題 + 即時訓練
Example + Instant Drill
少辣 基礎學習 ( 完成 1 + 2 + 3 )
加辣 高階學習 ( 完成 1 + 2 + 3 + 4 )
1 重要概念
3 例題 + 即時訓練
2 簡例 + 試算
廚師
推介
1 2 3