SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 9)


Question 9:
Diagram 4 shows a circle ADBC, with centre O and diameter 12 cm while sector ADC with the centre A and radius AD = 10 cm.

Diagram 4

By using π = 3.142,
find
(a) ∠BAC in radians, (2 marks)
(b) area, in cm2, of the shaded region. (3 marks)


Solution:
(a)

By using the cosine rule, 6 2 = 10 2 + 6 2 2( 10 )( 6 )cosBAC cosBAC= 10 2 + 6 2 6 2 2( 10 )( 6 ) cosBAC=0.8333 BAC= 33.56 o × π 180 o   =0.5857 rad


(b)

Area of sector CAD= 1 2 ( 10 ) 2 ( 0.5857×2 )    =58.57  cm 2 Area of yellow region =58.572( 1 2 ( 10 )( 6 )sin 33.56 o ) 1 2 absinC =58.5733.17 =25.40  cm 2 COD=( 0.5857×2 )×2    =2.3428 rad Area of shaded region =Area of sector CODBArea of yellow region = 1 2 ( 6 ) 2 ( 2.3428 )25.40 =16.77  cm 2

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