Trying to figure out what the radius of the large end of a cone would be, if it continued beyond it's actual physical length. (Hopefully I'm explaining this correctly.)

1) The small end of the cone is 12" in radius.
2) At 18.5" in length, The radius of the large end is 16".

If the cone continues to grow at the same rate, what will the radius of the large end be at 25.5" in length?

What is the equation to figure this out?
(I also need to figure this out for a cone that goes from 12" to 16" at 19.5" in length).

Thanks.

It's just similar triangles

12 + (length/18.5)*4

Can you dumb that down for me?...LoL

18.5 is the initial length, where the radius is 16"... I need to stretch the length to 25.5", and find the new radius.
The initial 16" radius doesn't come into the equation?
Are you saying it would be:

25.5 divided by 18.5,  multiplied by 4, plus 12 ?

Break everything down into rectangles and right triangles.
This may help w/ the trig, for future reference.

The radius of a cone increases at a constant rate - that is, every time you extend the length by an inch, the radius increases by a certain amount, and this amount doesn't change.  So you figure out how much it increases for every inch, and apply that to your added length.

In your case, the radius changes by 4 inches over the length of 18.5 inches.  So your radius increases by (4/18.5) inches per inch of length.  So over a total length of 25.5 inches, your radius will increase by 25.5 * (4 / 18.5), from an initial radius of 12 inches.  Your formula is therefore 12+(25.5*4/18.5)

Mike

@user55645 and @mike_c130 are both correct. They just use different ways to get there.
For me after finding the factor for the rate of increase it came down to a simple ratio problem.
 
    4               X
______ = _______

18.5              25.5


X = 5.513514

So the answer to the first problem is 17.513514

Assuming the projected length is the same in the second problem the ratio will be

         4                         X
____________ = __________

      19.5                    25.5

X = 5.23077

The solution is 17.23077

@ElrodCod
I don't dispute your way or the other posters'. The issue is the need to understand the work before you can make the relationships. If you don't understand how triangles make rectangles, opposite angles are congruent, a bit of trig, etc, you'll never know there's a ratio (shortcut) to be used.

Thank ALL of you!   Looking at all of these replies, I now understand completely.