0580/42 Feb/Mar 2024, Question 12: Arc Length
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks
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The question, in short
For a 12 cm radius circle with a 50° sector cut out, find the shaded shape's perimeter, then the height of a cylindrical cake of volume 3510 cm³ with that cross-section.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 4 marks
Work out the total distance around the shaded shape left after removing a 50° sector from a circle of radius 12 cm.
- 1Remaining angle = 360 − 50 = 310°
- 2Arc = 310/360 × 2 × π × 12 = 64.92… cm
- 3Perimeter = 12 + 12 + 64.92…
- 4= 88.92… ≈ 88.9 cm
Answer88.9 or 88.92 to 88.93...
Part (b) · 3 marks
Given the remaining cake volume is 3510 cm³, work out the height of the cylinder whose top is the shaded shape.
- 1Area of top = 310/360 × π × 12² = 389.55… cm²
- 2389.55… × h = 3510
- 3h = 3510 ÷ 389.55… = 9.010… ≈ 9.01 cm
Answer9.01 or 9.009 to 9.010…
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