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.

Answer 1

To find the volume of a cone, we use the formula:

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

where \( r \) is the radius and \( h \) is the height of the cone.

Given:
- The radius \( r = 12 \) feet.
- The height \( h \) is half the length of the radius. Therefore,

\[
h = \frac{1}{2} \times r = \frac{1}{2} \times 12 = 6 \text{ feet}.
\]

Now, we can substitute the radius and height into the volume formula:

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

Calculating \( (12)^2 \):

\[
(12)^2 = 144
\]

Now, substituting this value into the volume formula:

\[
V = \frac{1}{3} \pi (144)(6)
\]

Calculating \( 144 \times 6 \):

\[
144 \times 6 = 864
\]

Now substituting this back into the volume formula:

\[
V = \frac{1}{3} \pi (864)
\]

Using \( \pi = 3.14 \):

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

Calculating \( \frac{1}{3} \times 864 \):

\[
\frac{1}{3} \times 864 = 288
\]

Now substituting this into the formula:

\[
V = 3.14 \times 288
\]

Calculating \( 3.14 \times 288 \):

\[
3.14 \times 288 = 904.32
\]

Finally, rounding \( 904.32 \) to the nearest tenth:

\[
V \approx 904.3 \text{ cubic feet}
\]

Thus, the volume of Erik’s cone is

\[
\boxed{904.3} \text{ cubic feet}.
\]