To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Radius \( r = 14 \) mm
- Height \( h = 12 \) mm
- Using \( \pi \approx 3.14 \)
Now substitute the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (14^2) \times 12 \]
Calculating \( 14^2 \):
\[ 14^2 = 196 \]
Now substitute that back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 196 \times 12 \]
Now calculate \( 196 \times 12 \):
\[ 196 \times 12 = 2352 \]
So now we have:
\[ V = \frac{1}{3} \times 3.14 \times 2352 \]
Next, calculate \( 3.14 \times 2352 \):
\[ 3.14 \times 2352 = 7390.08 \]
Now divide by 3:
\[ V = \frac{7390.08}{3} \approx 2463.36 \]
Finally, rounding to the nearest hundredth, the volume of the cone is:
\[ \boxed{2463.36} \text{ cubic millimeters} \]