The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- \( r = 19 \) mm
- \( h = 15 \) mm
- Using \( \pi \approx 3.14 \)
Now, we can plug the values into the formula:
\[ V = 3.14 \times (19)^2 \times 15 \]
First, calculate \( (19)^2 \):
\[ (19)^2 = 361 \]
Now, substitute this back into the volume formula:
\[ V = 3.14 \times 361 \times 15 \]
Next, calculate \( 361 \times 15 \):
\[ 361 \times 15 = 5415 \]
Now, substitute this back into the volume formula:
\[ V = 3.14 \times 5415 \]
Finally, calculate \( 3.14 \times 5415 \):
\[ V \approx 17,004.1 \]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[ \boxed{17004.10} \text{ mm}^3 \]