Page 64 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure
9. (a) The diagram below shows sector MON with 2. It is known that the ratio of the area of a sector
centre O and sector PQN with centre Q. Sectors A to the area of a circle πr is equal to the ratio of
2
MON and PQN have radii of 5.8 cm and 3.9 cm the angle subtended at the centre of the circle, θ,
respectively. HOTS
Applying to the angle 2π which is A = q .
M πr 2 2π
P 2.7 rad 3. By using the equation A = q , the following
2.36 rad N πr 2 2π
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O Q formula can be derived to find the area of sector
Calculate the perimeter, in cm, of the shaded of a circle.
region. [Use π = 3.142]
(b) The diagram below shows sector OTU with For a circle with radius r, the area of sector of
centre O and a quadrant STV with centre S. a circle subtending the angle θ at the centre of
O HOTS Analysing the circle is A = r q.
1
2
2
V S
U
T SPM Tips
Given that the radius of sector OTU is 9 cm The value of q must be in radians when applying the
and S is the midpoint of the straight line OST. 1
2
Calculate the perimeter, in cm, of the shaded formula A = 2 r q.
region. [Use π = 3.142]
10. The diagram below shows a logo designed by
a logo designer for a type of online game. The
logo consists of a sector SROT with centre S 10
and a sector OMN with centre O. Given that
RM = 2MS, RM = 4 mm, ∠MOS = 0.18 rad and Calculate the area, A for each of the following sectors.
∠MSN = 1.46 rad. (a) (b)
R T HOTS Analysing O
M N 4.5 rad 4.52 cm 55.8º
S O 4.96 cm

O
Calculate the perimeter, in mm, for the whole logo. Solution
1
[Use π = 3.142] (a) A = r q
2
2
1
2
1.3 Area of Sector of a Circle = × (4.52) × 4.5
2
= 45.765 cm 2 Form 5
A Determining area of sector, radius
1
and angle subtended at the centre of (b) 55.8° = 55.8° × 3.142 2 rad
a circle 180°
= 0.9740 rad
1. A slice of pizza with the shape of a sector of a 1
2
circle is taken from one piece of pizza. The area A = r q
2
of a slice of pizza is equal to the area of a sector of
a circle. = 1 × (4.96) × 0.9740
2
2
= 11.98 cm
2
r
θ radian
Try Questions 1 - 2 in ‘Try This! 1.3’

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