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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

Log in to reply

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

Log in to reply

Nice.... Keep it up dude..

Log in to reply

Awesom man . ..

Log in to reply

Your solution is great!!!

Log in to reply

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

Log in to reply

Great!

Log in to reply