4024/22 May/Jun 2026, Question 23: Volume and Surface Area of a Cone
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 12 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
For a major sector with radius 9.1 cm and major arc 44 cm, work out the major angle, then treat the sector as a cone's curved surface to find its radius, volume, and the radius of a similar cone with volume 2387 cm³.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Determine the size of the major angle AOB using the given arc length and radius.
- 144 = x/360 × 2 × π × 9.1
- 2x = 44 × 360/(2 × π × 9.1)
- 3x = 277.0°
Answer276.99 to 277.2
Part (bi) · 2 marks
Demonstrate that the cone's base radius equals 7.0 cm to one decimal place.
- 1The arc becomes the circumference of the base
- 22πr = 44
- 3r = 44/(2π) = 7.0028…
- 4r = 7.0 cm (1 d.p.)
Answer7.00 or 7.001 to 7.003
Part (bii) · 4 marks
Work out how much space the cone occupies.
- 1Slant height = 9.1 cm
- 2h = √(9.1² − 7.0028…²) = 5.811…
- 3V = 1/3 × π × 7.0028…² × 5.811…
- 4V = 298 cm³
Answer298 or 298.2 to 298.5
Part (biii) · 3 marks
Given a mathematically similar cone holding 2387 cm³, find its base radius.
- 1Volume scale factor = 2387 ÷ 298.43… = 7.998…
- 2Length scale factor = ∛7.998… = 2.000…
- 3Radius = 7.0028… × 2.000… = 14.0 cm
Answer13.99 to 14.01
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 4024 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: 4024/22/M/J/26 · 4024_s26_qp_22 · 4024 s26 22 · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.