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,
- \( h \) is the height of the cylinder.
Given:
- Radius \( r = 8 \) millimeters,
- Height \( h = 13 \) millimeters.
Substituting in the values:
\[ V = \pi (8)^2 (13) \]
Calculating \( 8^2 \):
\[ 8^2 = 64 \]
Now substituting that back into the volume formula:
\[ V = \pi \times 64 \times 13 \]
Calculating \( 64 \times 13 \):
\[ 64 \times 13 = 832 \]
So now we have:
\[ V = \pi \times 832 \]
Using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 832 \approx 2617.76 \]
Rounding to the nearest hundredth gives:
\[ V \approx 2617.76 \]
Thus, the volume of the cylinder is approximately 2617.76 cubic millimeters.