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 of the base,
- \( h \) is the height of the cylinder.
Given:
- Radius \( r = 8 \) mm,
- Height \( h = 13 \) mm.
Now, substituting the values into the formula:
\[ V = \pi (8)^2 (13) \]
Calculating \( (8)^2 \):
\[ (8)^2 = 64 \]
Now substitute back into the formula:
\[ V = \pi \cdot 64 \cdot 13 \] \[ V = 832\pi \]
Now, using the approximation \( \pi \approx 3.14159 \):
\[ V \approx 832 \times 3.14159 \approx 2617.76 \]
Finally, rounding to the nearest hundredth:
\[ V \approx 2617.76 \text{ cubic millimeters} \]
Thus, the volume of the cylinder is approximately:
\[ \boxed{2617.76} \text{ cubic millimeters} \]