Circular Measure Long Questions (Question 1)


Question 1:
Diagram shows a circle, centre O and radius 8 cm inscribed in a sector SPT of a circle at centre P.  The straight lines, SP and TP, are tangents to the circle at point Q and point R, respectively.

[Use p= 3.142]
Calculate
(a) the length, in cm, of the arc ST,
(b) the area, in cm2, of the shaded region.            

Solution:
(a)
For triangle  O P Q sin 30 = 8 O P O P = 8 sin 30 = 16  cm Radius of sector  S P T = 16 + 8 = 24  cm S P T = 60 × 3.142 180 = 1.047  radian Length of arc  S T = 24 × 1.047 = 25.14  cm
(b)
For triangle  O P Q : tan 30 = 8 Q P P Q = 8 tan 30 = 13.86  cm Q O R = 2 ( 60 ) = 120 Reflex angle  Q O R = 360 120 = 240 240 = 3.142 180 × 240 = 4.189  radian Area of shaded region = (   Area of  sector  S P T ) ( Area of major    sector  O Q R ) ( Area of triangle  O P Q  and  O P R ) = 1 2 ( 24 ) 2 ( 1.047 ) 1 2 ( 8 ) 2 ( 4.189 ) 2 ( 1 2 × 8 × 13.86 ) = 301.54 134.05 110.88 = 56.61  cm 2

Leave a Reply

Your email address will not be published. Required fields are marked *