To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume of the cylinder,
- \( r \) is the radius of the base, and
- \( h \) is the height of the cylinder.
We are given:
- The volume \( V = 441\pi \) mm³,
- The radius \( r = 7 \) mm.
Now, we can substitute the values into the formula:
\[ 441\pi = \pi (7)^2 h \]
Next, we can simplify the equation. First, calculate \( (7)^2 \):
\[ (7)^2 = 49 \]
Now substitute this back into the equation:
\[ 441\pi = \pi \cdot 49 \cdot h \]
We can divide both sides of the equation by \( \pi \):
\[ 441 = 49h \]
Now, to solve for \( h \), we divide both sides by 49:
\[ h = \frac{441}{49} \]
Now we perform the division:
\[ h = 9 \]
Thus, the height of the cylinder is:
\[ \boxed{9 , \text{mm}} \]
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