To find the volume of a cone, we can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cone.
Given:
- Height \( h = 12 \) mm
- Diameter \( = 14 \) mm, so the radius \( r \) is half of the diameter:
\[ r = \frac{14}{2} = 7 \text{ mm} \]
Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (7)^2 \times 12 \]
First, calculate \( (7)^2 \):
\[ (7)^2 = 49 \]
Now substitute this back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]
Now calculate \( 49 \times 12 \):
\[ 49 \times 12 = 588 \]
Substituting this value back into the formula gives:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Calculating \( 3.14 \times 588 \):
\[ 3.14 \times 588 \approx 1845.92 \]
Now, divide by 3:
\[ V \approx \frac{1845.92}{3} \approx 615.3067 \]
Rounding this to the nearest hundredth gives:
\[ V \approx 615.31 \text{ cubic millimeters} \]
Thus, the volume of the cone is approximately 615.31 cubic millimeters.
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