The formula for the volume of a cone is
[tex]V=\frac{1}3\pi r^2h[/tex]
(you can remember it like this: it's literally just 1/3 the volume of a cylinder, just as a pyramid is 1/3 the volume of a prism)
We know that the diameter is 12...the radius is always half the diameter, so 6.
The height is 12.
Let's plug these into our volume formula.
[tex]V=\frac{1}3\pi \times6^2\times12[/tex]
[tex]V=\frac{1}3\pi \times36\times12[/tex]
[tex]V=\frac{1}3\pi \times432[/tex]
[tex]V=144\times \pi[/tex]
[tex]V\approx144\times3.14[/tex]
[tex]\boxed{V\approx452.16\ in^3}[/tex]
