Answer:
The cone's height is 9
Step-by-step explanation:
Recall that the volume of a cone is: [tex]\frac{h}{3} \pi \,r^2[/tex], where 'h' is the cone's height, and "r" the radius of its base.
In our case, we know that the volume of the cone equals; [tex]108\,\pi[/tex].
We also know the diameter of the base (12), so the radius of the base must be half of this: 6
Now we replace all known values in the formula for the volume, and solve for the unknown "h':
[tex]V=\frac{h}{3} \pi \,r^2\\108\,\pi =\frac{h}{3} \pi \,(6)^2\\108\,\pi =\frac{h}{3} \pi \,(36)\\108\,\pi =h (12) \pi \,\\h=\frac{108\,\pi }{12\,\pi } \\h=9[/tex]
