To find the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given that the diameter is 18 millimeters, the radius \( r \) is half of the diameter:
\[ r = \frac{d}{2} = \frac{18 , \text{mm}}{2} = 9 , \text{mm} \]
The height \( h \) is given as 18 millimeters. Now, substituting the values into the volume formula:
\[ V = \pi (9 , \text{mm})^2 (18 , \text{mm}) \] \[ V = \pi \times 81 , \text{mm}^2 \times 18 , \text{mm} \] \[ V = \pi \times 1458 , \text{mm}^3 \]
Using \( \pi \approx 3.14 \):
\[ V \approx 3.14 \times 1458 , \text{mm}^3 \] \[ V \approx 4577.32 , \text{mm}^3 \]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[ \boxed{4577.32} , \text{mm}^3 \]