Lemmara logoLemmaraWorked solution

0580/42 May/Jun 2022, Question 11: Volume and Surface Area of a Cone

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

A 28 cm by 20 cm rectangle is rolled into an open cylinder with AB joined to DC; find the base radius, the volume, an angle at point N, and a cone's slant height.

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

Part (ai) · 2 marks

Using AD = 28 cm as the circumference, show the cylinder radius rounds to 4.46 cm to 3 significant figures.

  1. 1Circumference = AD = 28 cm
  2. 22πr = 28, so r = 28 ÷ (2π)
  3. 3r = 4.456… = 4.46 cm (3 s.f.)

Answer4.455 to 4.456… = 4.46

Part (aii) · 2 marks

Find the volume of the cylinder using its radius and the 20 cm height.

  1. 1AD (28 cm) goes round the rim, so circumference 2πr = 28.
  2. 2r = 28 ÷ 2π = 4.456… cm. Height = AB = 20 cm.
  3. 3Volume = πr²h = π × 4.456…² × 20
  4. 4= 1247.7… ≈ 1250 cm³

Answer1250 or 1247 to 1249.9…

Part (aiii) · 3 marks

N is on the base with BN a diameter; find the angle between AN and the base.

  1. 1BN = 2 × 4.456… = 8.912… cm and AB = 20 cm is vertical
  2. 2tan ANB = 20 ÷ 8.912…
  3. 3Angle ANB = 65.98… ≈ 66°

Answer66 or 66.0 or 65.95 to 66.02

Part (b) · 5 marks

A cone has volume 310 cm³ and height twice its base radius; find its slant height.

  1. 1h = 2r, so 1/3 × π × r² × 2r = 310
  2. 2r³ = 310 × 3 ÷ (2π) = 148.0…, r = 5.289… cm
  3. 3h = 2 × 5.289… = 10.579… cm
  4. 4l² = 5.289…² + 10.579…² = 139.9…
  5. 5l = 11.82… ≈ 11.8 cm

Answer11.8 or 11.82 to 11.83

Stuck on a step? Read the free lesson: Volume and Surface Area of a Cone

Practise more volume and surface area of a cone questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on volume and surface area of a cone

Also searched as: 0580/42/M/J/22 · 0580_s22_qp_42 · 0580 s22 42 · question 11.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.