4PM1/02 Jan 2023, Question 9: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Cube with edge x cm has surface area A growing at 0.45 cm²/s. Find the rate of increase of volume in cm³/s when A is 384 cm².
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 7 marks
- 1dA/dt = 0.45
- 2V = x³, dV/dx = 3x²
- 3A = 6x², dA/dx = 12x
- 46x² = 384, x = 8
- 5dV/dt = dV/dx × dx/dA × dA/dt = 3x² × (1/(12x)) × 0.45 = 9x/80
- 6At x = 8: dV/dt = 0.9 cm³/s
Answer0.9 cm³/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 2 January 2023 · 4PM1/02 · 4pm1 jan23 2 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.