Question

the height is 12
the diameter is 14
What is the volume, in cubic millimeters, of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth.(1 point)
cubic millimeters

Answer 1

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**.