4MA1/1H Jan 2023, Question 21: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Find the volume of water passing through a pipe in 3 minutes, using a circular cross section with radius 4.8 cm, sector angle 72°, and flow speed 14 cm/s; give the answer in cm³ to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Sector area = (72/360) × π × 4.8² = 14.476…
- 2Triangle OAC area = ½ × 4.8² × sin 72° = 10.956…
- 3Shaded segment area = 14.476… − 10.956… = 3.520… cm²
- 43 minutes = 180 s, so length of water = 14 × 180 = 2520 cm
- 5Volume = 3.520… × 2520 = 8870 cm³
Answer8870
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