Problem 7 · 2011 Math Kangaroo
Medium
Spatial & Visual Reasoning
shadows-projections
A rectangular piece of paper is wrapped around a cylinder. Then an angled straight cut is made through the points X and Y of the cylinder, as shown on the left. The lower part of the paper is then unrolled. Which of the following pictures could show the result?
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Answer: C
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Hint 1 of 2
A slanted plane cut across a cylinder, then unrolled, gives a smooth wave rather than a straight or circular top.
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Hint 2 of 2
The unrolled cut is one period of a sine curve.
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Approach: unrolling a slanted cylinder cut gives a sine curve
- Wrapping height around the cylinder, a straight slanted cut becomes a sinusoid when the sheet is flattened.
- The lower piece therefore has a single smooth sine-shaped upper edge.
- That is picture C.
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