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Similarity, SMB-027

 


 

  1. What scale factor is used to convert Circle A into Circle B.   (1 mark)

  2. Complete this equation:
  3.      Area of Circle A = _____ × Area of Circle B.  (1 mark)

Show Answers Only
  1. \(\dfrac{1}{3}\)
  2. \(9\)
Show Worked Solution

i.     \(\text{Scale factor}\ = \dfrac{\text{Diameter B}}{\text{Diameter A}} = \dfrac{0.8}{2.4} = \dfrac{1}{3} \)
 

ii.     \(\text{Scale factor (B to A)} = \dfrac{\text{Diameter A}}{\text{Diameter B}} = \dfrac{2.4}{0.8} = 3 \)

\(\text{Scale factor (Area)} = 3^2 = 9 \)

\(\therefore\ \text{Area of Circle A = 9 × Area of Circle B} \)