Page 7 - 1202 Question Bank Additional Mathematics Form 5

13. The diagram shows a rhombus inscribed in a sector 14. The diagram shows a circle with centre O. PT and
SPM AOC with centre O and a radius of r. SPM QT are tangents to the circle at points P and Q
CLONE CLONE
respectively.
O C
β rad
r P
r cm T
A
B θ
Given that ∠AOC = β rad and the area of the sector is O Q
20 cm , express each of the following in terms of r.
2
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(a) The angle β. [3 marks]
(b) The perimeter, in cm, of the shaded region.
[2 marks] Given that the minor arc length PQ is 5 cm and
6
Answer: OT = — cm,
(a) θ
(a) express the radius, r of the circle in terms of θ,
[1 mark]
(b) find the area of the shaded region. [4 marks]
Answer:
(a)

(b)

(b)

Section B

15. The diagram shows a circular cross-section of a Answer:
container with centre O resting on two supports, each (a)
of height 25 cm. HOTS Applying

O
32 cm
A B

25 cm (b)
10 cm
The shortest distance of the container to the horizontal
surface is 10 cm. Given that the radius of the container
is 32 cm. Find
(a) the angle AOB, in radians, [4 marks]
(b) the area between the supports and the container.
[4 marks]

4 Question 14: 5
SOS TIP 44 Tangent PT = Tangent QT and ∠TPO = 90° 5 SOS TIP

Question 15:
(b) Area of the segment = Area of the sector AOB – Area of the triangle AOB

01_1202 QB AMath F5.indd 5 02/12/2021 8:44 PM