0580/42 Feb/Mar 2025, Question 23: Area of a Sector
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks
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The question, in short
Work out the volume of a tunnel 800 m long whose cross-section is a major circle segment of radius 2.5 m and height 3 m.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 7 marks
- 1The chord is 3 − 2.5 = 0.5 m from O, half-angle = cos⁻¹(0.5/2.5) = 78.46…°
- 2Angle at centre = 156.93…°, reflex angle = 203.07…°
- 3Major sector = 203.07…/360 × π × 2.5² = 11.08 m²
- 4Triangle = 1/2 × 2.5 × 2.5 × sin 156.93…° = 1.22 m²
- 5Segment area = 11.08 + 1.22 = 12.30 m²
- 6Volume = 12.30… × 800 = 9840.6 ≈ 9841 m³
Answer9835 to 9844
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