Question

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
hight 12mm radius 14mm

Answer 1

To find the volume of a cone, we 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:
- Radius \( r = 14 \) mm
- Height \( h = 12 \) mm
- Using \( \pi \approx 3.14 \)

Now substitute the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (14^2) \times 12
\]

Calculating \( 14^2 \):

\[
14^2 = 196
\]

Now substitute that back into the equation:

\[
V = \frac{1}{3} \times 3.14 \times 196 \times 12
\]

Now calculate \( 196 \times 12 \):

\[
196 \times 12 = 2352
\]

So now we have:

\[
V = \frac{1}{3} \times 3.14 \times 2352
\]

Next, calculate \( 3.14 \times 2352 \):

\[
3.14 \times 2352 = 7390.08
\]

Now divide by 3:

\[
V = \frac{7390.08}{3} \approx 2463.36
\]

Finally, rounding to the nearest hundredth, the volume of the cone is:

\[
\boxed{2463.36} \text{ cubic millimeters}
\]