Question

Erik measures a cone with a radius of 12 feet and a height that is half the length of the radius. What is the volume of Erik’s cone? Use 3.14 for pi and express your answer to the nearest tenth of a cubic foot.(1 point)
The volume of Erik’s cone is cubic feet.

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 \( r = 12 \) feet
- Height \( h = \frac{1}{2} \times r = \frac{1}{2} \times 12 = 6 \) feet

Now substituting the radius and height into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times (12^2) \times 6
\]

Calculating \( 12^2 \):

\[
12^2 = 144
\]

Now substituting that back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 144 \times 6
\]

Calculating \( 144 \times 6 \):

\[
144 \times 6 = 864
\]

Now substituting that in:

\[
V = \frac{1}{3} \times 3.14 \times 864
\]

Calculating \( 3.14 \times 864 \):

\[
3.14 \times 864 = 2716.16
\]

Finally, dividing by 3:

\[
V = \frac{2716.16}{3} \approx 905.38666667
\]

Rounding to the nearest tenth:

\[
V \approx 905.4
\]

Thus, the volume of Erik’s cone is approximately **905.4** cubic feet.