To find the volume \( V \) of a cone, you can use the following formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cone, and
- \( \pi \) is a constant approximately equal to 3.14.
Given:
- \( r = 14 \) mm,
- \( h = 12 \) mm,
- \( \pi \approx 3.14 \).
Now, plug the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (14)^2 \times 12 \]
First, calculate \( (14)^2 \):
\[ (14)^2 = 196 \]
Now, substitute this value back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 196 \times 12 \]
Calculate \( 196 \times 12 \):
\[ 196 \times 12 = 2352 \]
Now, substitute this back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 2352 \]
Calculate \( 3.14 \times 2352 \):
\[ 3.14 \times 2352 = 7394.88 \]
Now, divide by 3 to find the volume:
\[ V = \frac{7394.88}{3} \approx 2464.96 \]
Rounding to the nearest hundredth, the volume of the cone is:
\[ \boxed{2464.96} \text{ cubic millimeters} \]
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