Short Questions (Question 5 & 6)


Question 5:
Diagram below shows a sector QOR of a circle with centre O.

It is given that PS = 8 cm and QP = PO= OS = SR = 5 cm.
Find
(a) the length, in cm, of the arc QR,
(b) the area, in cm2, of the shaded region.

Solution:
(a) Length of arc QR = θ = 10 (1.75) = 17.5 cm

(b)
Area of the shaded region
= Area of sector QOR – Area of triangle POS
½ (10)2 (1.75) – ½ (5) (5) sin 1.75 (change calculator to Rad mode)
= 87.5 – 12.30
= 75.2 cm2



Question 6:
Diagram below shows a circle with centre O and radius 12 cm.

Given that A, B and C are points such that OA = AB and  ∠OAC = 90°, find
(a)   ∠BOC, in radians,
(b)  the area, in cm2, of the shaded region.   

Solution:
(a) For triangle OAC,
  cos  ∠AOC = 6/12 
  ÐAOC = 1.047 rad (change calculator to Rad mode)
  ÐBOC = 1.047 rad

(b) 
Area of the shaded region
= Area of BOC – Area of triangle AOC
½ (12)2 (1.047) – ½ (6) (12) sin 1.047 (change calculator to Rad mode)
= 75.38 – 31.17
= 44.21 cm2