if the diameter of a cone is 12, then its radius is half that, or 6.
[tex]\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=6\\
h=27
\end{cases}\implies V=\cfrac{\pi (6)^2(27)}{3}\implies V=324\pi [/tex]
