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:
- Volume \( V = 441\pi \) mm³
- Radius \( r = 7 \) mm
We can substitute the known values into the formula:
\[ 441\pi = \pi (7^2) h \]
First, calculate \( 7^2 \):
\[ 7^2 = 49 \]
Now substitute that into the equation:
\[ 441\pi = \pi (49) h \]
To simplify, we can divide both sides of the equation by \( \pi \):
\[ 441 = 49h \]
Next, solve for \( h \) by dividing both sides by 49:
\[ h = \frac{441}{49} \]
Now, calculate \( \frac{441}{49} \):
\[ h = 9 \]
Thus, the height of the cylinder is:
\[ \boxed{9 \text{ mm}} \]