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0606/21 Oct/Nov 2025, Question 9: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Use an isosceles triangle with equal sides 5 cm and base 8 cm to find angle θ in radians, then apply it to a shape made of two 5 cm radius arcs with height 8 cm.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Find the angle θ, in radians, between the two equal sides of 5 cm in the isosceles triangle with third side 8 cm.

  1. 1Split the triangle into two right-angled triangles: sin(θ/2) = 4/5
  2. 2θ = 2 sin⁻¹(4/5)
  3. 3θ = 1.85 radians

Answerθ = 1.85

Part (bi) · 2 marks

Using θ from part (a), find the perimeter of the shape formed by two arcs of radius 5 cm with height 8 cm.

  1. 1Each arc has radius 5 and subtends θ = 1.854… at its centre
  2. 2Arc length = 5 × 1.854… = 9.27…
  3. 3Perimeter = 2 × 9.27… = 18.5 cm

Answer18.5 cm

Part (bii) · 3 marks

Using θ from part (a), find the area of the shape bounded by the two arcs of radius 5 cm.

  1. 1Sector area = ½ × 5² × 1.854… = 23.18…
  2. 2Triangle area = ½ × 5² × sin 1.854… = 12
  3. 3Each segment = ½ × 5² × (θ − sin θ) = 11.18…
  4. 4Area of shape = 2 segments = 25(θ − sin θ) = 22.4 cm²

Answer22.4 cm²

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Also searched as: 0606/21/O/N/25 · 0606_w25_qp_21 · 0606 w25 21 · question 9.
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