0580/12 Feb/Mar 2023, Question 26: Circumference and Area of a Circle
Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 6 marks
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The question, in short
A circle has area 25π cm². Find its circumference in terms of π, then use two such circles as cylinder ends with total surface area 170π cm² to find the height h.
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Part (a) · 3 marks
Work out the circumference of the circle with area 25π cm², giving the answer in terms of π.
- 1πr² = 25π, so r² = 25 and r = 5
- 2Circumference = 2 × π × 5 = 10π cm
Answer10π
Part (b) · 3 marks
Two of these circles form the ends of a cylinder of height h cm and total surface area 170π cm²; find h.
- 1Total surface area = 2 × 25π + 10π × h = 170π
- 210πh = 170π − 50π = 120π
- 3h = 12
Answer12
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