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Similarity, SMB-025

A triangular prism is pictured below.
 

By what factor will its volume change if

  1. Each dimension is doubled?   (1 mark)

  2. Each dimension is decreased by two-thirds?   (2 marks)
Show Answers Only
  1. \(\text{Increases by a factor of 8}\)
  2. \(\text{Decreases by a factor of}\ \ \dfrac{1}{27} \)
Show Worked Solution

i.    \(\text{Dimensions increase by a factor of 2}\)

\(\Rightarrow\ \text{Volume increases by a factor of}\ 2^3 = 8\)
 

ii.    \(\text{Dimensions decrease by two-thirds}\)

\(\Rightarrow\ \text{i.e. adjust dimensions by a factor of}\ \ \dfrac{1}{3} \)

\(\Rightarrow\ \text{Volume decreases by a factor of}\ \Big{(} \dfrac{1}{3} \Big{)}^3 = \dfrac{1}{27} \)