4MA1/1HR Jun 2022, Question 20: Area 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
Two similar statues A and B; B's volume is 20% less than A's. Find k, the percentage by which B's surface area is less than A's, to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Volume scale factor = 1 − 0.20 = 0.8
- 2Length scale factor = ∛0.8 ≈ 0.9283
- 3Area scale factor = (0.9283)² ≈ 0.8617
- 4Percentage of area B compared to A = 0.8617 × 100 ≈ 86.17%
- 5k = 100 − 86.17 = 13.83
- 6k = 13.8
Answer13.8
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