Page 12 - PBD Plus Matematik Tambahan T5 (EG)

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

SP 1.2.3 Menyelesaikan masalah yang melibatkan panjang lengkok.

7. Selesaikan masalah yang melibatkan panjang lengkok. TP 5
Solve the problems involving the arc lengths.
Contoh
A
Rajah menunjukkan sebuah sektor AOB berpusat O. Diberi AC = CO = 3.4 cm dan
/ACO = 1.5 rad. Cari perimeter rantau berlorek itu.
The diagram shows a sector AOB with centre O. Given that AC = CO = 3.4 cm and /ACO = 1.5 rad. Find the
perimeter of the shaded region.
O Panjang lengkok/Arc length = 4.63 × 0.82
B C
= 3.8 cm
/ACO = 1.5 rad = 85.94° Perimeter rantau berlorek = 3.4 + 3.8 + (4.63 –3.4)
/AOB = π – 1.5 = 0.82 rad Perimeter of the shaded region = 8.43 cm
2
Jejari/Radius
3.4 + 3.4 – 2(3.4) kos 85.94
AO = √
2
2
2
= 4.63 cm
8Penerbitan Pelangi Sdn. Bhd.
(a) A Rajah menunjukkan dua sektor, AOD dan BOC berpusat O. Diberi 2OA = 3OB, OA = 9.6
cm dan /AOD = 2.2 rad. Cari perimeter rantau berlorek itu.
B
The diagram shows two sectors, AOD and BOC with centre O. Given that 2OA = 3OB , OA = 9.6 cm and /AOD
= 2.2 rad. Find the perimeter of the shaded region.
O
C
D
2
OB = (9.6) = 6.4 cm Panjang lengkok BC = 6.4(2.2) = 14.08 cm
3 Arc length
Panjang lengkok AD = 9.6(2.2) = 21.12 cm
Arc length Perimeter rantau berlorek = 21.12 + 14.08 + 2(9.6 – 6.4)
Perimeter of the shaded region = 41.6 cm

(b)
P Rajah menunjukkan satu sektor dengan pusat O. Sebuah bulatan dicangkum di
B 7
dalamnya dengan pusat P. Diberi jejari bulatan ialah 4 cm dan /APB = π rad. Cari
A 8
The diagram shows a sector with centre O. A circle with centre P is inscribed in it. Given that the radius of the
O 7
circle is 4 cm and /APB = π rad, find
8
(i) jejari sektor. (ii) luas rantau berlorek.
the radius of the sector. the area of the shaded region.
7
(i) /OPB = π × 1 kos / cos 78°459 = 4
2 OP
= 7 π rad OP = 4 = 20.5 cm P 4 B
16 kos 78°459 7 _ π rad
= 78° 459 A 8
\ Jejari sektor = 20.5 + 4
Radius of the sector = 24.5 cm O
π
7
(ii) /POB = – 7 π Sudut major APB = 2π – π
2 16 Major angle APB 8
= π = 9π
16 8
= 11.25°
\ Luas rantau berlorek / Area of the shaded region
4
1
2 9π
= 22.5° × π(24.5) – 2 3 1 (4)(20.5) sin 78°459 – (4)  2
2
360° 2 2 8
= 9.17 cm 2
Cuba jawab Praktis SPM 1, K1: S5
TAHAP PENGUASAAN 1 2 3 4 5 6 5 © Penerbitan Pelangi Sdn. Bhd.