Projecting a surface segment of a cone onto a 2D plane?

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Firstly, I'd like to apologise - I do not know the correct terms for what I am asking.

Assume that the top/bottom of the highlighted portion there is actually aligned with the base.

To help explain: I need to wrap that section of the cone using a piece of paper. What shape (exactly) do I need to cut out from said paper so that it will wrap flawlessly?

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2 Answers

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If I've understood your problem correctly, I think this should help. This one's a right circular cone and its opened up paper version. Here we've taken an arbitrary curved surface of the form shown on the cone and visualized.

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Since the distance from the apex to the base is constant. Assuming the cone is made of paper, cutting it open along your yellow line will make a circular sector whose radius is the former distance. Your cross-sections will correspond to bands concentric with the sector's circumference.

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