Page 23 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

PBD 1.2 Panjang Lengkok Suatu Bulatan Buku Teks
PBD
PBD
Arc Length of a Circle ms. 5 – 11

FOKUS TOPIK

1. Panjang lengkok, s, suatu bulatan berkadaran dengan sudut 3. Panjang lengkok bulatan, s, dapat ditentukan dengan
yang tercangkum di pusat bulatan. menggunakan
The arc length, s of a circle is directly proportional to the size of the The arc length of a circle, s, can be determined by using
angle subtended at the centre of the circle.
s = jq
2. Secara am. kita boleh tulis seperti yang berikut:
In general, we can write as follows: dengan j ialah jejari bulatan dan q radian ialah sudut
q° q rad panjang lengkok (arc length) tercangkum oleh lengkok di pusat bulatan.
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360° = 2π rad = lilitan bulatan (circumference) where j is the radius of the circle and q radian is the angle
subtended by the arc at the centre of the circle.
dengan panjang lilitan = 2πj dan jejari ialah j unit.
where the circumference = 2πj and the radius is j units.

3. Tentukan panjang lengkok, s bagi setiap bulatan yang diberi. SP 1.2.1 TP1
Determine the arc length, s for each of the following given circles.
Guna/Use p = 3.142.

(a) (b)
A A
s
B
A
0.8 rad 2.62 rad S θ 7π
__
O s O
7.4 cm 5
O
13.2 cm
4.5 cm
B B
Panjang lengkok, s = jq Panjang lengkok, s = jq q = 2p – 7p
Arc length Arc length 5
s = 7.4 × 0.8 s = 13.2 × 2.62 = 3p
5
= 5.92 cm = 34.58 cm
Panjang lengkok, s = jq
Arc length
s = 4.5 × 3p
5
= 8.483 cm

(c) (d) (e)
A s A A
B 6.8 cm
1.6 rad 105°32’ 13.7 cm
O 5.2 cm O O 0.76 rad
θ B θ
s s B

Panjang lengkok, s = jq q = 360° – 105° 329 q = (2π – 0.76) rad
Arc length = 254° 289
s = 5.2 × 1.6 = 254.47° Panjang lengkok, s = jq
= 8.32 cm Arc length
s = 13.7 × (2p – 0.76)
q° = s
360° 2πj = 75.68 cm
q° = s
360° 2π(6.8)
254.47° × 2π(6.8)
s =
360°
= 30.21 cm

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