Page 37 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat
2. Rajah menunjukkan sebuah bulatan dan sektor 3. Rajah menunjukkan satu cermin OPQR dan
berpusat O. bahagian berlorek ialah kayu hiasan yang terdiri
The diagram shows a circle and a sector with centre O. daripada dua sektor OPQR yang berpusat O dan
Q QPOR yang berpusat Q dengan jejari sama, j.
P The diagram shows a mirror OPQR and the shaded area of a
decorative wood frame which is made up of two sectors, OPQR
O θ with centre O and QPOR with centre Q and of the same radius, j.
S
KBAT Menganalisis
R
P
Diberi panjang lengkok PS dan QR masing-
masing ialah 3 cm dan 8 cm dan SR = 9.5 cm. Cari
Given the arc length PS and QR are 3 cm and 8 cm respectively O Q
and SR = 9.5 cm. Find
(a) jejari bulatan dan sudut q dalam radian.
the radius of circle and the angle q in radians. R
[3 markah / 3 marks]
(b) luas rantau berlorek itu. (a) Tunjukkan bahawa /POR = 2π radian.
the area of the shaded region. Show that /POR = 2π radian. 3
[4 markah / 4 marks] 3 [5 markah / 5 marks]
Jawapan / Answer : (b) Cari jumlah perimeter kayu hiasan jika jejari
(a) 3 = jq .................a sektor ialah 0.5 m.
8 = (j + 9.5) q .................b Find the total perimeter of the decorative wood if the
radius of the sector is 0.5 m.
b ÷ a: [3 markah / 3 marks]
8 = j + 9.5 Tip KBATKBAT
3 j KBAT
5j = 9.5 × 3 Perhatikan bahawa OP = OQ = OR.
j = 5.7 cm Maka, keempat-empat tembereng ialah bersaiz
sama.
3
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= 0.53 rad.
It is observed that OP = OQ = OR.
Hence, the four segments are equal in size.
5.7 = 30.37°
(b) Luas rantau berlorek = Luas ∆OQR – Luas Jawapan / Answer :
sektor POS (a) Oleh sebab/ Since
Area of the shaded region = Area ∆OQR – Area of sector OP = PQ = OQ
POS Maka/ Hence /POQ
= 60°
1 1 π
= (9.5 + 5.7) sin 30.37° – (5.7) (0.53) =
2
2
2 2 3
= 49.79 cm 2 /POR = 2π rad.
3
(b) panjang lengkok PQ
arc length of PQ
π
= 0.5  2 = π cm
3 6
Jumlah perimeter
Total perimeter
π
= 4(0.5) + 4  2 = 4.09 m
6

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