# Finding the radius of a cone at an arbitrary height?

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I'm trying to find the radius of a cone at an arbitrary height. I'm stuck but I'm pretty sure there has to be a way to do it. Here's what I have so far... I have a cone with a height (h), a top radius (r1), a base radius (r2), and a length of the edge of the cone from base to top (len). I can find len = root( (r2 - r1)^2 + h^2 ). Now given the height (h') at which to find the radius (r'). I figure that a non-zero top radius shouldn't be too tricky to handle. I'll subtract r2 - r1, perform my calculations and then add r1 to r'. I also could perform some trig to get the angle. With all these values, I'm still coming up short because I have two unknowns: r' and len'. What's my next step?

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No sooner than I hit send did I have an inspiration. I think this will work so tell me what you think.

If I find the percentage of the distance between h and h', then I can use the same percentage on r2' [I think].

So here are my calculations:
r2' = r2 - r1percentage = h' / hr' = (r2' * percentage) + r1

How does that look? It's cheap as hell compared to the other calculations I was considering.

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r' = r2-(h'/h)(r2-r1)
Is that what you're looking for?

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Yes, that's quite close to what I had here and fixed the problem I just noticed as well. So much easier than I originally thought it would be. Thanks!

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Rutin
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