Page 10 - Module & More Matematik Tambahan Tg5

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

6. Tentukan perimeter tembereng bagi setiap bulatan berpusat O yang berikut
Determine the perimeter of the segment of each of the following circles with centre O. TP 4

CONTOH (a)
P 1
9.6 cm

O
O 6.2 cm P Q 0.4 rad BAB
2 rad

Q
0.4π × 360°
0.4π rad =
Penyelesaian: 2π
Perentas PQ dapat diperolehi dengan petua = 72°
kosinus, iaitu PQ = j + j − 2j kos q , dengan q Maka/Then,
2
2
2
dalam darjah. PQ = 9.6 + 9.6 − 2(9.6) kos72°
2
2
2
The length of the chord PQ can be obtained by using the = 11.28 cm
cosine rule, that is PQ = j + j − 2j cos q , such that q Panjang lengkok PQ = jq
2
2
2
is in degree.
Arc length PQ = 9.6(0.4π)
2 × 360°
2 rad = = 114.59° = 12.06 cm
2π Perimeter = (12.06 + 11.28) cm
Maka/Then, = 23.34 cm
PQ = 6.2 + 6.2 − 2(6.2) kos 114.59°
2
2
2
= 10.43 cm
Panjang lengkok PQ = jq = 6.2(2)
Arc length PQ
= 12.4 cm
Perimeter = (12.4 + 10.43) cm = 22.83 cm
(b) (c)
P
8 cm P 3 cm 4.5 rad
O O
30 cm Q Q

Panjang lengkok minor PQ = 2π(8) – 30
Minor arc length PQ = 20.27 cm Panjang lengkok minor PQ = 2π(3) – 4.5(3)
Minor arc length PQ = 5.35 cm
∠POQ = 20.27 ∠POQ = 2π − 4.5
8 = 1.78 rad
= 2.53 rad = 102.17°
= 145.14° Maka, PQ = 3 + 3 − 2(3) kos102.17°
2
2
2
Maka, PQ = 8 + 8 −2(8) kos145.14° = 4.67 cm
2
2
2
= 15.27 cm Perimeter = 5.35 cm + 4.67 cm
Perimeter = 15.27 + 20.27 = 10.02 cm
= 35.54 cm

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