AQA · Mathematics · 8300
GCSE Maths: Similar shapes: area
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Similar shapes: area (Corbettmaths Video 293), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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If two shapes are similar with a length scale factor of k, what is the area scale factor?
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k²
If two shapes are similar with a length scale factor of k, what is the volume scale factor?
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k³
For similar shapes, if the area scale factor is m, then the length scale factor is ?.
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√m
For similar shapes, if the volume scale factor is n, then the length scale factor is ?.
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∛n
Two similar shapes have a length ratio of 3:5. What is their area ratio?
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9:25 (square each term of the length ratio)
Two similar shapes have a length ratio of 3:5. What is their volume ratio?
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27:125 (cube each term of the length ratio)
Two similar solids have an area ratio of 4:49. What is their length ratio?
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2:7 (take the square root of each term)
Two similar solids have a volume ratio of 27:1000. What is their length ratio?
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3:10 (take the cube root of each term)
For similar 3D shapes, does the surface area scale with the length scale factor or the volume scale factor?
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The length scale factor (specifically, surface area scales as length²)
Two similar shapes have surface areas in ratio 25:81. What is the length of the larger shape if the smaller is 30 cm?
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54 cm (length ratio is 5:9, so 30 × 9/5 = 54)
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