4MA1/2HR Jun 2023, Question 24: Volume and Surface Area of a Sphere
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Sphere A has surface area nine times sphere B's; their volumes differ by 117π cm³. Work out the radius of the smaller sphere, showing all steps.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Let the radius of sphere B (smaller) be r, so radius of sphere A is 3r (since surface area ratio = 9:1, and surface area ∝ r², so linear scale factor = √9 = 3)
- 2Volume of sphere B = (4/3)πr³
- 3Volume of sphere A = (4/3)π(3r)³ = (4/3)π×27r³ = 36πr³
- 4Difference in volume = 36πr³ − (4/3)πr³ = (108πr³ − 4πr³)/3 = (104πr³)/3
- 5Given difference = 117π
- 6So (104πr³)/3 = 117π
- 7Divide both sides by π: (104r³)/3 = 117
- 8Multiply both sides by 3: 104r³ = 351
- 9r³ = 351 / 104
- 10r³ = 3.375
- 11r = ∛3.375
- 12r = 1.5
Answer1.5
Stuck on a step? Read the free lesson: Volume and Surface Area of a Sphere
Practise more volume and surface area of a sphere questions
Real 4MA1 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 sphere
Also searched as: 4MA1 2HR June 2023 · 4MA1/2HR · 4ma1 jun23 2hr · question 24.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.