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Puzzle of the Week #197 - Volcano Climb

April 12, 2019 Elliott Line
volcano sketch 3.JPG

An expedition is being planned to climb a truncated conical volcano that is 40km diameter at the base, and 24km diameter at the crater edge. The slope length is 12km.

The path starts at A at the base and ends at point B on the crater edge, exactly halfway round the volcano from A.

What is the length of the shortest possible route around the conical face of the volcano (to the nearest km)?

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