Page 23 - PBD Plus Matematik Tambahan T5 (EG)

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

3. Rajah menunjukkan satu cermin OPQR dan 4. y
bahagian berlorek ialah kayu hiasan yang terdiri
daripada dua sektor OPQR yang berpusat O dan D
QPOR yang berpusat Q dengan jejari sama, j. A(0, 6) E
The diagram shows a mirror OPQR and the shaded area of a P
decorative wood frame which is made up of two sectors, OPQR O B x
with centre O and QPOR with centre Q and of the same radius, j. C(0, –4)
SP 1.4.1 KBAT Menganalisis
Rajah menunjukkan satu semibulatan PADB
P berpusat P dan sektor CAB berpusat C dilukis pada
satah Cartes. Diberi CP = 5√ 3 unit, cari SP 1.4.1
The diagram shows a semicircle PADB with centre P and a sector
O Q
CAB with centre C drawn on a Cartesian plane. Given that CP =
5 3 unit, find
(a) diameter semibulatan itu.
R the diameter of the semicircle.
[2 markah / 2 marks]
(a) Tunjukkan bahawa /POR = 2π radian. (b) sudut ACB, dalam radian.
Penerbitan Pelangi Sdn. Bhd.
2π 3 the angle ACB, in radians.
Show that /POR = radian.
3
[5 markah / 5 marks] [2 markah / 2 marks]
(b) Cari jumlah perimeter kayu hiasan jika jejari (c) perimeter rantau berlorek.
sektor ialah 0.5 m. the perimeter of the shaded region.
Find the total perimeter of the decorative wood if the [3 markah / 3 marks]
radius of the sector is 0.5 m. (d) luas rantau berlorek.
[3 markah / 3 marks] the area of the shaded region.
[3 markah / 3 marks]
TIP Menjawab
Perhatikan bahawa OP = OQ = OR.
Maka, keempat-empat tembereng ialah bersaiz (a) CP = 5√ 3
sama. CA = 10 = CB
It is observed that OP = OQ = OR.
10 – 25 × 3
2
Hence, the four segments are equal in size. \ AP = √
= 5 units
Jawapan / Answer : Diameter AB = 10 units

(a) Oleh sebab/ Since (b) sin ∠PCB = 5 = 1
OP = PQ = OQ 10 2
Maka/ Hence /POQ ∠PCB = 30°
= 60° ∠ACB = 60° = rad
π
= π 3
3
/POR = 2π rad. (c) Panjang lengkok ADB = π(5) unit
3 Arc length ADB
(b) panjang lengkok PQ π
arc length of PQ Panjang lengkok AEB = (10) unit
3
Arc length AEB
π
= 0.5  2 = π cm
3 6 Perimeter rantau berlorek = 10 π + 5π
Jumlah perimeter Perimeter of the shaded region 3
Total perimeter = 26.18 unit
π
= 4(0.5) + 4  2 = 4.09 m (d) Luas rantau berlorek
6
Area of the shaded region
= luas semibulatan – luas tembereng
area of semicircle – area of segment
1
2 π
= 1 π(5) – 3 1 (10) – (10 ) sin 60° 4
2
2
2 2 3 2
= 30.21 unit 2

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