0606/22 May/Jun 2026, Question 12: Connected Rates of Change and Small Changes
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
A sphere's volume V and radius r are in cm units, with r changing over time t. At the moment when the rate of change of V is 9 times the rate of change of r, work out V.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1V = (4/3)πr³, so dV/dr = 4πr²
- 2dV/dt = dV/dr × dr/dt, so dV/dr = 9
- 34πr² = 9, r = 3/(2√π) (r > 0)
- 4V = (4/3)π(3/(2√π))³ = 9/(2√π) ≈ 2.54
AnswerV = 9/(2√π) (2.54)
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 0606 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: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 12.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.