To find the height of the cylinder, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- \( V = 54\pi , \text{cm}^3 \)
- \( r = 3 , \text{cm} \)
We can substitute the values into the volume formula:
\[ 54\pi = \pi (3)^2 h \]
Simplifying this, we find:
\[ 54\pi = \pi (9) h \]
Now, divide both sides by \( \pi \):
\[ 54 = 9h \]
Next, solve for \( h \):
\[ h = \frac{54}{9} = 6 , \text{cm} \]
Therefore, the height of the cylinder is:
\[ \boxed{6 , \text{cm}} \]
So the answer is D. 6 cm.