0580/42 Feb/Mar 2022, Question 9: Volume and Surface Area of a Cone
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Use the cone's volume and base radius to find the sector angle when the cone is opened out, then find a tank's capacity in litres from pipe flow data.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 6 marks
Given volume 95.4 cm³ and radius 2.4 cm, find the cone's slant height and base circumference, then calculate the sector angle x°.
- 195.4 = 1/3 × π × 2.4² × h, so h = 95.4 × 3 ÷ (π × 2.4²) = 15.81… cm
- 2Slant height l = √(15.81…² + 2.4²) = 15.99… cm
- 3Arc length = base circumference: x/360 × 2 × π × 15.99… = 2 × π × 2.4
- 4x = 360 × 2.4 ÷ 15.99…
- 5x = 54.00… ≈ 54.0°
Answer54.0 or 53.99 to 54.03…
Part (b) · 4 marks
A pipe of diameter 8 cm carries fuel at 2 m/s for 24 minutes; calculate the tank capacity in litres.
- 1Cross-section area = π × 4² = 50.26… cm²
- 2Length of fuel in 24 min = 200 cm/s × 24 × 60 s = 288 000 cm
- 3Volume = 50.26… × 288 000 = 14 476 458… cm³
- 4÷ 1000: 14 476.4… litres ≈ 14 500 litres
Answer14500 or 14470 to 14480
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 LemmaraMore past-paper questions on volume and surface area of a cone
Also searched as: 0580/42/F/M/22 · 0580_m22_qp_42 · 0580 m22 42 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.