Length of wraps around a cylinder.
The picture shows a cylinder with a radius of 7 units with a red string wrapped 5 times around it. If the rise between the strings-turns on the cylinder is 1 unit,
What is the length of the string wrapped around the cylinder to 3 decimal places ?
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1 solution
The picture above shows a Cylinder with a wrapped red string. Unwrap the cylinder and you end up with a rectangle, whose width is 2\pi r and the height is d\cdot n where d is the distance between the strings and n is the number of sections which is the same as the number turns of the string around the cylinder.
You can use the Pythagorean theorem to get, the length of red string in each section to be \sqrt{4\pi^2 r^2 + d^2} and in total we have n\sqrt{4\pi^2 r^2 + d^2}.