Question

A cone is shown with a height of 12 mm and a radius of 14 mm
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

The volume \( V \) of a cone can be calculated using the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

Where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone, and
- \( \pi \) is approximately 3.14.

Given:
- \( r = 14 \) mm,
- \( h = 12 \) mm,
- \( \pi \approx 3.14 \).

Now, plug in the values into the volume formula:

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

First, calculate \( (14)^2 \):

\[
(14)^2 = 196
\]

Now substitute back into the volume equation:

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

Now calculate \( 196 \times 12 \):

\[
196 \times 12 = 2352
\]

Next, substitute this value back into the equation:

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

Now calculate \( 3.14 \times 2352 \):

\[
3.14 \times 2352 = 7396.48
\]

Finally, divide by 3:

\[
V = \frac{7396.48}{3} \approx 2465.43
\]

Rounding to the nearest hundredth, the volume of the cone is:

\[
\boxed{2465.43} \text{ cubic millimeters}
\]