well, if its base has a diameter of 12, that means its radius is half that, or 6.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ V=1086 \end{cases}\implies 1086=\cfrac{\pi (6)^2 h}{3}\implies 3528=36\pi h \\\\\\ \cfrac{3528}{36\pi }=h\implies 31.19\approx h[/tex]
