Arc length between two points on a cylinder

rww88

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Mar 20, 2017
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How does one determine the arc length between points A and B shown on the cylinder diagrams below?
 

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After thought

I think I may have solved my own problem. Unroll the cylinder and get the two dimensional figure shown below (second image). Here the arc length is simply equal to x / cos theta. Does anybody agree with this solution? If so, what would be the arc length between points A and B if the dimension y shown in the top figure is given?
 

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After thought

I think I may have solved my own problem. If the cylinder is "rolled-out" you get the figure shown in the second figure below. Here the arc length between points A and B is simply equal to x/cos theta. Does anyone agree with this solution? If so, what is the equation for the distance between points A and B if the dimension y shown in the first figure is given?
 

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