Create a procedural cone

Good morning,
I want to make a procedural cone with the ability to change the diameter of the Base.

I tried by making two circles and a line :


Then in the Object data panel of the line, setting the taper and Bevel Object :


It works if it's static. However, if I animate the size of the bevel Object Circle, when I compile the scene, my cone doesn't change.

Is there any workaround ?

Regards,
Seb

Hello
Could you try to use Shape Keys?

But currently it works only with smooth shading
If this workaround is OK for you, I can build the exporter, which can use both shading models (flat and smooth).

Thank you Roman !
It works :)

What's about the flat shading?

Hi !
I wanted a smooth shading so it's OK for me ;)