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Australian AMC 2011 - Senior Question 23

AMC AUSTRALIA · Australian AMC 2011 - Senior

Question 23

An irrational spider lives at one corner of a closed box which is a cube of edge 1 metre. The spider is not prepared to travel more than $\sqrt2$ metres from its home (measured by the shortest route across the surface of the box). Which of the following is closest to the proportion (measured as a percentage) of the surface of the box that the spider never visits?
  1. 20%
  2. 25%
  3. 30%
  4. 35%
  5. 50%