The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder, and
- \( \pi \) is approximately \( 3.14159 \).
Given:
- Height \( h = 13 \) mm,
- Radius \( r = 8 \) mm.
Substituting the values into the formula, we have:
\[ V = \pi (8^2)(13) \]
Calculating \( 8^2 \):
\[ 8^2 = 64 \]
Now substituting back:
\[ V = \pi (64)(13) \]
Calculating \( 64 \times 13 \):
\[ 64 \times 13 = 832 \]
Now substituting this result into the volume formula:
\[ V = \pi \times 832 \]
Using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 832 \approx 2617.99368 \]
Rounding this to the nearest hundredth, we get:
\[ V \approx 2617.99 \text{ cubic millimeters} \]
So the volume of the cylinder is approximately:
\[ \boxed{2617.99} \text{ cubic millimeters} \]