Similar Areas & Volumes (OCR GCSE Maths): Revision Note

Similar areas & volumes

How do I find the length, area or volume scale factors of similar shapes?

• The scale factor (SF) for a given quantity (length, area or volume), can be found by dividing the quantity on one shape by the quantity on the other shape

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• An object could be made either bigger or smaller by a scale factor

  • When k > 1, the object is getting bigger

    • This is also true for k² > 1 and k³ > 1

  • When 0 < k < 1, the object is getting smaller

    • This is also true for 0< k² < 1 and 0 < k³ < 1

What is the connection between the scale factors for lengths, areas and volumes of similar shapes?

• The length, area and volume scale factors are powers with the same base number

• If the length scale factor is k then

  • The area scale factor is k²

  • The volume scale factor is k³

• If you know one scale factor, you can find the scale factors

  • If you have the length scale factor

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  • If you have the area scale factor

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  • If you have the volume scale factor

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How do I find missing lengths, areas and volumes for similar shapes?

• STEP 1
  Identify the equivalent known quantities

  • Recognise if the quantities are lengths, areas or volumes

• STEP 2
  Find the scale factor from two known lengths, areas or volumes

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• STEP 3
  Use the scale factor you have found to find other required scale factor(s)

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• STEP 4
  Multiply or divide by relevant scale factor to find the missing quantity

  • Think about whether the quantity should be bigger or smaller than the given quantity