Trying to Create Cone from Image

I am attempting to take a circular image (a logo of something) and edit it so that it can be printed and turned into a small cone.  I have spent HOURS researching this and cannot seem to find the the problem.  I've followed the steps below (found on a tutorial at another website) and the gap (where the circle gets slid under itself to create the cone shape) is so small.  I have messed around with it since this morning and am at my wit's end.  Thank you, in advance, for any assistance! 
Let's consider my avatar as the original image. I make sure it is cropped into a circle.
Then in photoshop, I do Filter->Distort->Polar coordinates->Polar to rectangular:
Then, I resize the contents (but not the container [e.g. select all, edit->transform->scale]) of the image horizontally. The percentage I reduce is the percentage of degrees I will remove:
Finally, I go back to polar coordinates, and retrim as a circle:  (OP: I don't know what they mean by "retrim as a circle," though, so I stop after selecting "rectangular to polar")
Wrapping the image around the removed wedge is an exercise left to the reader.

Thank you for your reply, Nancy!  I actually want to print this and then "assemble" it into a cone.
Here is the original tutorial.  The original person was able to accomplish exactly what I want...I just can't figure out where I'm going wrong!
http://design.tutsplus.com/tutorials/illustrate-a-traffic-cone-icon-in-photoshop--psd-121

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    1
    2
    3
    4
    5
    6
    - create processor for the image datasource ...
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    Step 1) Copy that code into a .java file
    Step 2) Compile it
    Step 3) Run it
    Step 4) Look at the output
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