Problem 7 · 2017 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracingspatial-reasoning
A circle with radius 1 rolls along a straight line from point K to point L, as shown, with \(KL = 11\pi\). In which position is the circle when it has arrived in L?
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Answer: E
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Hint 1 of 2
How many full turns does the circle make over a length of 11π?
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Hint 2 of 2
Its circumference is 2π, so see how much of an extra turn is left over.
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Approach: count revolutions, then read off the leftover part-turn
- A radius-1 circle has circumference 2π, so over 11π it makes 11π ÷ 2π = 5.5 turns.
- The half turn left over flips the shaded pattern to the opposite side compared with the start.
- Reading off the resulting orientation gives choice E.
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