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Similar Areas and Volumes Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Similar shapes
Shapes that have the same shape but different sizes, with corresponding angles equal and corresponding sides in proportion.
Scale factor (length)
The ratio of the lengths of corresponding sides in similar shapes.
Area scale factor
The square of the length scale factor. Used to compare the areas of similar shapes.
Volume scale factor
The cube of the length scale factor. Used to compare the volumes of similar 3D shapes.
Length ratio to area ratio
If the length ratio is a:b, the area ratio is a²:b².
Length ratio to volume ratio
If the length ratio is a:b, the volume ratio is a³:b³.
Finding missing lengths in similar shapes
Use the length scale factor to calculate unknown side lengths by multiplying or dividing.
Finding missing areas in similar shapes
Use the area scale factor to calculate unknown areas by multiplying or dividing.
Finding missing volumes in similar shapes
Use the volume scale factor to calculate unknown volumes by multiplying or dividing.
Key property of similar shapes
Corresponding angles are equal, and corresponding sides are proportional.
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