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SPM Additional Mathematics 2019, Paper 2 (Question 3)


Question 3:
Diagram 1 shows a sector POA with centre O.

It is given that the length of arc PB is 2.56 cm. [Use π = 3.142]
Calculate
(a) ∠ POB in radians, [2 marks]
(b) the area, in cm2, of the shaded region. [4 marks]


Solution:
(a)
s=rθ 2.56=10θ θ=0.256 radian

(b)
Area of OBP = 1 2 r 2 θ = 1 2 × 10 2 ×0.256 =12.8  cm 2 AC 10 =tan 60 o AC=17.32 Area of shaded region ABC =( 1 2 ×10×17.32 )( 1 2 × 10 2 × π 3 ) =34.233  cm 2 Total area of shaded regions =12.8+34.233 =47.033  cm 2

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