To find the answer, we first need to understand the formula to find the volume of a cone:
Volume = 1/3 x base area x height
In this case, we can put the given information into the formula.
The base area of the cone: pi(radius)^2 = pi(3)^2 = 9pi
We can then find the height:
27pi = 1/3 x 9pi x height
27pi/9pi = 1/3 x height
3 = 1/3 x height
height = 9
Therefore, the height is 9cm.
Hope it helps!