Page 16 - Matematik Tam_Modul A+_Pan Asia Publications

2. Rajah menunjukkan sebuah sektor AOB berpusat O. 3. Rajah menunjukkan dua sektor, POQ dan SOR,
The diagram shows a sector AOB at centre O. berpusat O.
Cari/Find The diagram shows two sectors, POQ and SOR, with centre O.
S
P
A B
130°
7.5 cm O θ
O
(a) ∠AOB dalam radian,
∠AOB in radians, Q
(b) perimeter, dalam cm, sektor AOB. R
the perimeter, in cm, of the sector AOB. Diberi bahawa OP = 6 cm, nisbah OP : OS = 2 : 3 dan
2
KBAT Menilai luas rantau berlorek ialah 33.75 cm , cari
[3 markah/marks] Given that OP = 6 cm, the ratio of OP : OS = 2 : 3 and the
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area of the shaded region is 33.75 cm , find
2
(a) 130° × π = 2.27 rad (a) panjang OS.
the length of OS,
180°
(b) Perimeter = 7.5 +7.5 + 7.5(2.27) (b) nilai q, dalam radian,
= 32.02 cm the value of q, in radians. KBAT Menganalisis
[4 markah/marks]
2
(a) OP = = 6 = OS = 9 cm
OS 3 OS
1
(b) 1 (9) q – (6) q = 33.75
2
2
2 2
22.5q = 33.75
q = 1.5 rad

4. Rajah menunjukkan dua konsentrik bulatan berpusat 5. Rajah menunjukkan sebuah segi tiga sama sisi OPQ dan
KLON O. Sudut yang dicangkum pada pusat O oleh lengkok titik S yang terletak di dalam segi tiga itu dengan keadaan
SPM
major PQ ialah 8p rad dan perimeter bagi seluruh rajah OS = SP = SQ.
ialah 48 cm. The diagram shows an equilateral triangle OPQ and the
The diagram shows two concentric circles with centre O. point S lies inside the triangle such that OS = SP = SQ.
The angle subtended at the centre O by the major arc PQ is O
8p rad and the perimeter for the whole diagram is 48 cm.
12 cm
P
A S
O P Q
B Q
X
3
Diberi OP = OA, OA = j cm dan ∠POQ = 4p rad, Diberi bahawa S ialah pusat bagi sektor SPXQ dan
2
ungkapkan j dalam sebutan p. panjang lengkok PXQ ialah 12 cm. Cari perimeter
3 rantau berlorek dalam sebutan π dan ! 3.
Given OP = OA, OA = j cm and ∠POQ = 4p rad, express Given that S is the centre of the sector SPXQ and the length of
2
j in terms of p. KBAT Menganalisis arc PXQ is 12 cm. Find the perimeter of the shaded region in
[4 markah/marks] π and ! 3 . KBAT Menganalisis
3
OP = OA
2 [4 markah/marks]
3
= j 6
2 kos OPS = PS
3
Panjang lengkok major PQ = j(8p) 6
2 kos 30° =
= 12jp PS 6 6 12
Panjang lengkok AB = j(4p) PS = kos 30° = ! 3 = ! 3 = 4! 3 cm
= 4jp 2
Jumlah perimeter: Perimeter rantau berlorek
3
12jp + 4jp + 2( j – j) = 48 π
2 = 4! 3 + 4! 3 + (4! 3)( 120° × )
16jp + j = 48 180°
j(16p + 1) = 48 = 8! 3 + 8! 3 π 6
j = 48 3 30° 120°
(
16p + 1 = 8! 3 1 + π ) cm 12
3
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