Similar Areas & Volumes (AQA GCSE Maths)

What are similar shapes?

• Two shapes are mathematically similar if one is an enlargement of the other
• If two similar shapes are linked by the scale factor, k
  
  • Equivalent areas are linked by an area factor, k²
  • Equivalent volumes are linked by a volume factor, k³

How do I work with similar shapes involving area or volume?

• STEP 1
  Identify the equivalent known quantities
  • These could be for lengths, areas or volumes
• STEP 2
  Establish direction
  • Are they getting bigger or smaller?
• STEP 3
  Find the Scale Factor from two known lengths, areas or volumes
  • Second Quantity ÷ First Quantity
  • Check the scale factor is > 1 if getting bigger and < 1 if getting smaller
  • If the scale factor, s.f., is from two lengths, write it as k = s.f.
  • If the scale factor, s.f., is from two areas, write it as k² = s.f.
  • If the scale factor, s.f., is from two lengths, write it as k³ = s.f.
• STEP 4
  Use the value of the scale factor you have found to convert other corresponding lengths, areas or volumes using
  • Area Scale Factor = (Length Scale Factor)² 
    • Or Length Scale Factor = √(Area Scale Factor)
  • Volume Scale Factor = (Length Scale Factor)³ 
    • Or Length Scale Factor = ∛(Volume Length Factor) 
• Use the scale factor to find a new quantity