Page 61 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

C Solving problems involving arc 9
length The diagram below shows a logo designed by Azlan for
a new electronic product. The logo consists of sector
8 OABC with centre O and sector BPQ with centre B.
The diagram below shows a sector ABC with centre B
B and a sector CDE with centre E. Sectors ABC and
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
CDE have radii of 4 cm and 2.2 cm respectively. A P O
Q C
A 3
Given that OA = OP, OP = 3.2 cm,
C 2
D E 2.38 rad ∠BOP = 1.85 rad and ∠PBQ = 0.99 rad. Calculate the
1.43 rad perimeter, in cm, of the whole logo.
B
Solution
3
OA = OP
Calculate the perimeter, in cm, of the shaded region. 2
3
[Use π = 3.142] = (3.2)
2
Solution = 4.8 cm
s = rq s = rq ∠AOC major = 1.85 × 2
CD
AC
= 4 × 1.43 = 2.2 × 2.38 = 3.7 rad
= 5.72 cm = 5.236 cm s ABC = rq
= 4.8 × 3.7
∠BED = 3.142 – 2.38 = 17.76 cm
= 0.762 rad For ∆BOP,
BP = OP
For ∆BDE, sin ∠BOP sin ∠OBP

BD = DE BP = 3.2
sin ∠BED sin ∠DBE sin 1.85 sin 1 0.99 2
BD = 2.2 2
sin 0.762 sin 1.43 BP = 3.2 × sin 1.85
BD = 2.2 × sin 0.762 sin 1 0.99 2
sin 1.43 2
= 1.534 cm = 6.476 cm
AD = AB – BD s = rq
PQ
= 4 – 1.534 = 6.476 × 0.99
= 6.411 cm
Form 5
= 2.466 cm
AP = CQ
= 4.8 – 3.2
Perimeter of the shaded region = 1.6 cm
= s + s + AD
CD
AC
= 5.72 + 5.236 + 2.466 Perimeter of the whole logo
= 13.422 cm = s ABC + s + AP + CQ
PQ
= 17.76 + 6.411 + 1.6 + 1.6
Try Question 9 in ‘Try This! 1.2’ = 27.371 cm
Try Question 10 in ‘Try This! 1.2’

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