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)

\begin{array}{l} s = r θ \\ 2.56 = 10 θ \\ θ = 0.256 radian \end{array}

(b)

\begin{array}{l} Area of O B P \\ = \frac{1}{2} r^{2} θ \\ = \frac{1}{2} \times 10^{2} \times 0.256 \\ = 12.8 {cm}^{2} \\ \frac{A C}{10} = \tan 60^{o} \\ A C = 17.32 \\ Area of shaded region A B C \\ = (\frac{1}{2} \times 10 \times 17.32) - (\frac{1}{2} \times 10^{2} \times \frac{π}{3}) \\ = 34.233 {cm}^{2} \\ Total area of shaded regions \\ = 12.8 + 34.233 \\ = 47.033 {cm}^{2} \end{array}

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