Problem 16 · 2016 Math Kangaroo
Stretch
Geometry & Measurement
perimeter
Jack wants to keep six tubes each of diameter 2 cm together using a rubber band. He chooses between the two possible variations shown. How are the lengths of the rubber bands related to each other?
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Answer: E — Both bands are equally long.
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Hint 1 of 2
Each band is straight segments plus curved arcs that wrap the outer tubes.
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Hint 2 of 2
The arcs always join to one full circle; compare only the straight parts.
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Approach: straight parts plus one circle
- In both arrangements the curved pieces add up to exactly one full circle (2π).
- The straight pieces trace the outline of the centres; both layouts give the same total straight length of 12.
- So the two bands are equally long.
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