0580/22 Oct/Nov 2025, Question 23: Volume and Surface Area of a Cone
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 7 marks
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The question, in short
Major sector AOB has radius 12 cm and sector angle 240°. Show the major arc length is 16π cm, then form a cone and find its volume in the form (a√b)π/3.
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Part (a) · 1 mark
Show that the major arc AB has length 16π cm using radius 12 cm and sector angle 240°.
- 1Major arc AB = 240/360 × 2 × π × 12
- 2= 2/3 × 24π = 16π cm
Answer240/360 × 2 × π × 12
Part (b) · 6 marks
The sector is curved into a cone; work out its volume, giving the answer as (a√b)π/3 with a an integer and b prime.
- 1Arc becomes the base circumference: 2πr = 16π, so r = 8 cm
- 2Slant height = 12 cm, so 12² = 8² + h²
- 3h² = 144 − 64 = 80, h = √80 = 4√5 cm
- 4V = 1/3 × π × 8² × 4√5
- 5= (256√5)π/3 cm³
Answer(256√5)π/3
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Also searched as: 0580/22/O/N/25 · 0580_w25_qp_22 · 0580 w25 22 · question 23.
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