MODUL SUKATAN MEMBULAT 1.3 LUAS SEKTOR SUATU BULATAN V1

MATEMATIK TAMBAHAN
( ADDITIONAL MATHEMATICS)

SUKATAN MEMBULAT
( CIRCULAR MEASURE)

DISEDIAKAN OLEH :
MOHD NOR FADHLI BIN AZIZ
JAMIL BIN TARMIZI
FAZIRA BINTI MOKHTAR
NURHIDAYAH BINTI ISMAIL

1.3 LUAS SEKTOR SUATU BULATAN
AREA OF SECTOR OF A CIRCLE

(1.3.1-Menentukan luas sektor , jejari dan sudut tercangkum di pusat bulatan)
(1.3.1-Determine the are of sector, radius and angle substended at the centre of a circle)

Nota

Luas sektor minor

Area of minor sector

πr2  θ , θ = darjah/degree
3600

Luas sektor minor
Area of minor sector

1 r2θ , θ = radian
2

1. Hitungkan luas rantau berlorek bagi setiap rajah berikut : TP2
Calculate the area of the shaded region in each of the folloing diagrams. TP2

(a)

1 r2θ  1 52   

22

[17.5 cm2]
(b)

[12.25 cm2]
(c)

Modul Sukatan Membulat / Circular Measure_T5 [86.40 cm2]
Page 1

(d)

[94.58 cm2]
2. Suatu bulatan yang berjejari 5 cm mempunyai lengkok 8 cm. Hitung luas sektor yang

dicangkum oleh lengkok itu. TP3
A circle of radius 5 cm has an arc length of 8 cm. Calculate the area of the sector.
TP3

[20cm2]
3. Diberi luas sektor berlorek sebuah bulatan ialah 64 cm2. Hitung jejari bulatan itu. TP2

Given that the area of the shaded sector of a circle is 64 cm2. Calculate the radius of
the circle. TP2

1  r 2  1800  π   64 cm2
2  

r2  192
π

r

r

Modul Sukatan Membulat / Circular Measure_T5 [7.818cm]
Page 2

4. Diberi θ dan A masing – masing mewakili sudut dan luas sektor suatu bulatan. Cari jejari
bagi setiap bulatan itu. TP2

Given θ and A represent the angle and area of a sector of a circle respectively. Find the
radius of each of the circles. TP2

(a) A  36 cm2, θ  0.6rad

[10.95 cm]

(b) A  66 cm2, θ  1.8rad

[8.563 cm]

(c) A  11.8 cm2, θ  2500

(d) A  67 cm2, θ  1200 [2.326 cm]
Modul Sukatan Membulat / Circular Measure_T5
[7.998 cm]
Page 3

(e) A  49.5 cm2, θ  0.4π rad

[8.876 cm]

(f) L  100 cm2, θ  0.75π rad

[9.213 cm]

5. Diberi luas sektor berlorek ialah 80 cm2, cari sudut θ dalam radian.
Given that the area of the shaded sector is 80 cm2, find the central angle θ in radian

A  1 r2θ
2

= 1  2 θ

2


[3.787 rad]

6. Diberi r dan A masing – masing mewakili jejari dan luas sektor suatu bulatan. Cari sudut
sektor bagi setiap bulatan itu. TP2

Given r and A represent the radiis and area of a sector of a circle respectively. Find the
angle of each of the circles. TP2

(a) A  54cm2, r  7 cm

A  1 r2θ
2

= 1  2 θ

2


Modul Sukatan Membulat / Circular Measure_T5 [2.204rad]
Page 4

(b) A  98cm2, r  5.6 cm [6.25 rad]
(c) A  160 cm2, r  10 cm [3.2 rad]
(d) A  50.8 cm2, r  4.3 cm [5.495rad]
(e) A  124 cm2, r  12.5 cm [1.587 rad]
(f) A  198 cm2, r  9.6 cm [4.297 rad]

Modul Sukatan Membulat / Circular Measure_T5 Page 5

7. Rajah menunjukkan dua sektor OEH dan OFG yang berpusat sepunya, O. OEF dan OHG
ialah garis lurus. Diberi OE = 6 cm, EOH 1.1 rad dan luas sektor OFG ialah tiga kali
luas sektor OEH, cari

The diagram shows two sectors, OEH and OFG with centre O. OEF and OHG are straight

lines. Given OE = 6 cm, EOH 1.1 rad and the area of sector OFG is 3 times the area of

sector OEH, find

(a) luas rantau berlorek, / the area of the shaded region,

(b) panjang OF. / the length of OF.

Modul Sukatan Membulat / Circular Measure_T5 [(a) 39.6 cm2 (b0 10.39 cm]
Page 6