Edexcel International GCSE Mathematics A · 4MA1
Similarity
Similar shapes have equal corresponding angles and proportional corresponding lengths. Area and volume scale differently from length. Match corresponding sides carefully, especially when a diagram rotates or reflects one of the shapes.
Key method
If the length scale factor is k, the area factor is k² and the volume factor is k³. Recover a length factor from an area ratio by taking its square root.
Worked example
Two similar solids have corresponding lengths in ratio 2:3. The smaller has volume 40 cm³. Find the larger volume.
- The enlargement factor from smaller to larger is 3/2.
- Cube the factor: (3/2)³ = 27/8.
- Multiply the smaller volume by 27/8.
Answer and interpretation
135 cm³.
Common mistake
Multiplying volume by 3/2 uses the length factor instead of the volume factor.
Practise independently
Similar triangles have areas 18 and 50. Find their corresponding length ratio.
Check your answer
√(18/50) = 3/5, so the ratio is 3:5.
Syllabus connection
This lesson develops similarity within the geometry area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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