To find the volume \( V \) of a cone, the formula is:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
From your description, it seems you have the following values:
- The radius \( r = 7 \) mm
- The height \( h = 12 \) mm
Now we can substitute these values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (7)^2 \times 12 \]
Calculating \( (7)^2 \):
\[ (7)^2 = 49 \]
Now substituting that into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]
Calculating \( 49 \times 12 \):
\[ 49 \times 12 = 588 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Next, we calculate \( 3.14 \times 588 \):
\[ 3.14 \times 588 = 1847.92 \]
Now divide by 3:
\[ V = \frac{1847.92}{3} \approx 615.9733 \]
Rounding to the nearest hundredth gives:
\[ V \approx 615.97 \text{ cubic millimeters} \]
So the volume of the cone is approximately 615.97 cubic millimeters.