Problem 3 · 2023 Math Kangaroo
Medium
Geometry & Measurement
spatial-reasoning
A cylindrical tin is 15 cm high. The circumference of the base circle is 30 cm. An ant walks from point A at the base to point B at the top. Its path is partly vertically upwards and partly along horizontal circular arcs. Its path is drawn in bold on the diagram (with a solid line on the front and a dashed line at the back). How long is the total distance covered by the ant?
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Answer: E — 75 cm
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Hint 1 of 2
The bold path is made only of straight vertical pieces and horizontal arc pieces.
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Hint 2 of 2
Add up all the vertical climbs (they total the height) and all the horizontal arcs (each is part of the 30 cm circumference) separately.
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Approach: separate the path into vertical rises and horizontal arc lengths
- Every vertical piece of the path together climbs the full height of 15 cm.
- The horizontal arcs each cover part of the 30 cm circumference; following the drawn path they sum to 60 cm.
- Total distance = 15 + 60 = 75 cm.
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