Page 14 - PBD Plus Matematik Tambahan T5 (EG)

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

9. Tentukan jejari bagi sektor bulatan berlorek yang berikut. Beri jawapan betul kepada dua tempat perpuluhan.
Determine the radius of the following shaded sectors of circles. Give your answer correct to two decimal places. TP 4
Contoh
Diberi luas sektor yang berlorek ialah (a) Diberi luas sektor ialah 49 cm 2 2

23.8 cm 2 Given the area of the sector is 49 cm .
Given the area of the shaded sector is 23.8 cm . 2
A
1.63 rad
1.78 rad
O
B
Tip Penting 49 = 1.63
luas sektor q πj 2 2π
Guna luas bulatan = 2π
2
23.8 = 1.78 Use area of sector = q j = 49 × 2
1.63
πj 2 2π area of circle 2p j = 7.75 cm
j = 23.8 × 2
2
1.78
j = 5.17 cm

(b) Diberi luas sektor berlorek ialah 7.5 cm . (c) P
2
Given the area of the shaded sector is 7.5 cm . Diberi luas sektor berlorek ialah
2
2
P 30 cm dan panjang lengkok
O 18 cm
5π major PQ ialah 18 cm.
___
6 Given the area of the shaded sector is
O Q 30 cm and the major arc length is 18 cm.
2
Q
Tip Penting
18
πj – 30
2
5π

=
 2 Penerbitan Pelangi Sdn. Bhd. Guna/ Use
7.5 = 2 6 2πj πj 2 panjang lengkok luas sektor
πj 2 2π j = 2(πj – 30) lilitan bulatan = luas bulatan
2
5π 2 18 arc length = area of sector
7.5 = 3 2 πj – 30 = 9j circum ference area of circle
πj 2 2π πj – 9j – 30 = 0 2
(–9) – 4π(–30)
j = 7.5 × 2 × 3 j = 9 √
2
5π 2π
j = 1.69 cm j = 4.84 cm
10. Tentukan sudut tercangkum, q dalam radian, di pusat bulatan bagi setiap yang berikut. Beri jawapan betul
kepada dua tempat perpuluhan jika perlu. TP 4
Determine the subtended angle, q in radians, at the centre of the circle for each of the following. Give your answer correct to two decimal
places where necessary.
Contoh
Diberi luas sektor berlorek (a) Diberi luas sektor berlorek
4.8 cm ialah 23 cm 2 ialah 15.7 cm dan berjejari
2
O θ Given the area of the shaded sector θ 4.2 cm.
is 23 cm . O Given the area of the shaded sector is
2
15.7 cm and with radius 4.2 cm.
2
23 = q 15.7 = 2π – q
π(4.8) 2 2π π(4.2) 2 2π
q = 23 × 2 q = 2π – 15.7 × 2
(4.8) 2 (4.2) 2
= 1.99 rad = 4.50 rad

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