WAEC Mathematics 2014 Theory — Question 18
Question 18 of 23 from the West African Examinations Council (WAEC) Mathematics 2014 Theory paper, with the correct answer and a full explanation.
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10(b). In the diagram, M and N are the centres of two circles of equal radii 7cm. The circles intersect at P and Q. If ∠PMQ=∠PNQ=60°, calculate, correct to the nearest whole number, the area of the shaded portion. [Take π=22/7]
Model answer
Sector area (60°, r=7) = (60/360)×(22/7)×7² = (1/6)×154 = 25.67cm² Triangle MPQ is equilateral (MP=MQ=7=radius, angle 60°): Area = (√3/4)×7² ≈ 21.22cm² Segment area (one side) = 25.67−21.22 = 4.45cm² Total shaded (lens) area = 2×4.45 ≈ 8.9cm² ≈ 9cm²
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