4PM1/01R Jun 2025, Question 11: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 8 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Water enters a vertical cone of radius 3 m and height 4 m at 9π m³/s; find the rate of rise of water height when h = 2 m.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 8 marks
- 1Similar triangles: r/h = 3/4, so r = 3h/4
- 2V = (1/3)π(3h/4)²h = 3πh³/16
- 3dV/dh = 9πh²/16
- 4dh/dt = dV/dt × dh/dV = 9π × 16/(9πh²)
- 5At h = 2: dh/dt = 16/4 = 4 m/s
Answer4 m/s
Stuck on a step? Read the free lesson: Connected Rates of Change and Small Changes
Practise more connected rates of change and small changes questions
Real 4PM1 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 connected rates of change and small changes
Also searched as: 4PM1 1R June 2025 · 4PM1/01R · 4pm1 jun25 1r · question 11.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.