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 $\sqrt{4\pi^2r^2+h^2}$ .

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

#Geometry #Cylinders #3D #Easymoney #Spirals

Easy Math Editor

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Comments

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

Arron Kau Staff - 6 years, 8 months ago

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

Trevor Arashiro - 6 years, 8 months ago

Nice.... Keep it up dude..

Sanjeet Raria - 6 years, 8 months ago

Great!

Kashif Ahmad - 6 years, 8 months ago

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

tasnia nowrin - 6 years, 7 months ago

Your solution is great!!!

Daniel Osmena - 6 years, 7 months ago

Awesom man . ..

Sumit Kumar - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$