To find the volume of a cylinder, the formula is given by:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder.
In this case, you've provided:
- Height \( h = 13 \) mm
- Radius \( r = 8 \) mm
Now we can plug these values into the formula:
\[ V = \pi (8 , \text{mm})^2 (13 , \text{mm}) \]
Calculating \( (8 , \text{mm})^2 \):
\[ (8 , \text{mm})^2 = 64 , \text{mm}^2 \]
Now, substituting this back into the volume formula:
\[ V = \pi (64 , \text{mm}^2) (13 , \text{mm}) = \pi (832 , \text{mm}^3) \]
Now, calculating the volume:
\[ V \approx 3.14159 \times 832 , \text{mm}^3 \approx 2618.9837 , \text{mm}^3 \]
Rounding to the nearest hundredth:
\[ V \approx 2618.98 , \text{mm}^3 \]
Thus, the volume of the cylinder is approximately 2618.98 cubic millimeters.