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GCE Mathematics 1990 Question 18

Question 18

Mensuration of Plane Shapes

In the diagram below, O is the centre of the circle with radius 10cm, and ∠ABC = 30°. Calculate, correct to 1 decimal place, the length of arc AC. (Take π = 3.14)

Diagram for this question
  1. A.5.2cm
  2. B.10.5cm
  3. C.13.2cm
  4. D.20.6cm
  5. E.31.4cm
Show the answer and explanation

Answer: B (10.5cm)

Explanation

The angle at the centre is twice the angle at the circumference: ∠AOC = 60°. Arc AC = 60/360 × 2 × 3.14 × 10 = 10.47 ≈ 10.5cm.