It depends on what information you have on the cone.
If you know the volume of the cone as well as its height, you could use the formula for the volume of a cone to find the radius, multiply that by 2, and find the diameter.
The formula is: $${\mathtt{V}} = \left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{r}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{h}}$$ (the volume equals one-third times pi times the radius squared, times height.)
If you have the area or circumference of the cone's base, use the formulas for area and circumference of a circle.
Circumference: $${\mathtt{C}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{d}}$$
Area: $${\mathtt{A}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{r}}}^{{\mathtt{2}}}$$
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