Generalized length of 3D Cylindrical spiral: NO CALC NEEDED!

In one of my previous problems, I posted finding the length of a spiral stair case. I always wondered how to find the length of a 3D spiral if every segment was congruent to every other. I never thought to visualize it as a cylinder.

Above, you can see the spiral and the cylinder's net. The height of the cylinder is the height of the rectangle and the circumference of the circle is the width. By the pythagorean theorem, the length of one spiral will be 4π2r2+h2\sqrt{4\pi^2r^2+h^2}.

Now, since all parts are congruent, we can multiply it by the degree of turning (1 spiral =360 or 2π2\pi) relative to one turn. Tus our final formula is 4π2r2+h2(θ360)\sqrt{4\pi^2r^2+h^2}\left(\frac{\theta}{360}\right) where θ\theta is the degree of turning.

Note by Trevor Arashiro
5 years, 1 month ago

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And this is why we love math. Thanks for sharing.

Arron Kau Staff - 5 years, 1 month ago

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Wow, thank you so much. That means a lot to me. :D

Trevor Arashiro - 5 years, 1 month ago

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Nice.... Keep it up dude..

Sanjeet Raria - 5 years, 1 month ago

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Great!

Kashif Ahmad - 5 years, 1 month ago

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Too cool!!!thanks for sharing.totally loved it

tasnia nowrin - 5 years, 1 month ago

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Your solution is great!!!

Daniel Osmena - 5 years, 1 month ago

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Awesom man . ..

Sumit Kumar - 4 years, 10 months ago

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