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0580/42 May/Jun 2023, Question 5: Volume and Surface Area of a Cone

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 13 marks

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The question, in short

Cone with base diameter 8 cm and height 15 cm; cylinder of radius 0.45 m filled with 300 litres at 375 ml per second. Find cone volume, label percentage, filling time and water height.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Calculate the volume of the cone using radius from the 8 cm diameter and height 15 cm.

  1. 1r = 8 ÷ 2 = 4 cm
  2. 2V = 1/3 × π × 4² × 15 = 80π
  3. 3= 251.3… ≈ 251 cm³

Answer251 or 251.3 to 251.4

Part (aii) · 5 marks

Find the curved surface area of the cone as a percentage of its total surface area.

  1. 1l = √(4² + 15²) = √241 = 15.52… cm
  2. 2Curved surface = π × 4 × 15.52… = 195.08… cm²
  3. 3Total surface = 195.08… + π × 4² = 195.08… + 50.26… = 245.34… cm²
  4. 4Percentage = 195.08… ÷ 245.34… × 100 = 79.51… ≈ 79.5%

Answer79.5 or 79.51…

Part (bi) · 3 marks

Find the time in minutes and seconds to pour 300 litres at 375 ml per second.

  1. 1300 litres = 300 000 ml
  2. 2Time = 300 000 ÷ 375 = 800 seconds
  3. 3800 s = 13 × 60 + 20 = 13 min 20 sec

Answer13 min 20 sec

Part (bii) · 3 marks

Calculate the height of water in the cylinder of radius 0.45 m holding 300 litres.

  1. 1300 litres = 0.3 m³
  2. 2π × 0.45² × h = 0.3
  3. 3h = 0.3 ÷ 0.6361… = 0.4715… ≈ 0.472 m

Answer0.472 or 0.4715 to 0.4716…

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Also searched as: 0580/42/M/J/23 · 0580_s23_qp_42 · 0580 s23 42 · question 5.
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