GCSE Maths (AQA)

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Similarity & Volume

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Geometry and Measures Mensuration and Calculation

Similarity & Volume

5:05 Similarity Calculations
Spec R12 G19
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  • For similar 3D shapes with a length ratio of 1 to n, the ratio of the volumes is 1 to n cubed
  • Two shapes are similar if one shape is a larger or smaller version of the other shape
  • All corresponding angles will be the same and all corresponding lengths will be in the same proportion
  • The length ratio of two similar cuboids can be expressed using a ratio
  • The volume ratio of two similar cuboids is given by 1 to n cubed, where n is the length ratio
  • The volume of a cuboid can be calculated by multiplying the length, width, and height together
  • The volume ratio holds true for all 3D shapes, not just cuboids
  • The volume of the larger cuboid is equal to n cubed times the volume of the smaller cuboid
  • The volume ratio can be used to calculate the volume of a larger shape given the volume of a smaller shape and the length ratio
  • In the example given, the volume of the larger house is calculated using the volume ratio and the volume of the smaller house

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