4MA1/1HR Jan 2022, Question 18: Volume Factor of Similar Shapes
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
Three similar solids A, B, C have surface area ratio A:B = 4:9 and volume ratio B:C = 125:343. Find the simplest ratio of the height of A to the height of C.
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Solution · 4 marks
- 1Area ratio A : B = 4 : 9, so the length ratio is √4 : √9 = 2 : 3
- 2Volume ratio B : C = 125 : 343, so the length ratio is ∛125 : ∛343 = 5 : 7
- 3Match B: A : B = 10 : 15 and B : C = 15 : 21
- 4A : C = 10 : 21
Answer10 : 21
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