To find the volume of a cone, you can 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:
- Height (\( h \)) = 12 mm
- Diameter = 14 mm, so the radius (\( r \)) = \frac{14}{2} = 7 mm
Now plug the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]
Calculating \( 7^2 \):
\[ 7^2 = 49 \]
Now substitute \( 49 \) back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]
Calculating \( 49 \times 12 \):
\[ 49 \times 12 = 588 \]
Now our formula looks like this:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Calculating \( 3.14 \times 588 \):
\[ 3.14 \times 588 = 1847.92 \]
Now divide \( 1847.92 \) by \( 3 \):
\[ V = \frac{1847.92}{3} = 615.9733333 \]
Finally, rounding to the nearest hundredth:
\[ V \approx 615.97 \]
So the volume of the cone is approximately 615.97 cubic millimeters.
1 answer