Question

A cone-shaped container on a farm is used for storing animal feed. The container has a radius of 4 ft and a height of 12 ft. The volume of feed, in cubic feet, this container can store is:

Answer 1

To calculate 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 of the cone.

Given:
- Radius \( r = 4 \) ft
- Height \( h = 12 \) ft

Now, substitute the values into the formula:

\[
V = \frac{1}{3} \pi (4)^2 (12)
\]

First, calculate \( (4)^2 \):

\[
(4)^2 = 16
\]

Now, substitute back into the equation:

\[
V = \frac{1}{3} \pi (16)(12)
\]

Next, calculate \( 16 \times 12 \):

\[
16 \times 12 = 192
\]

Now substitute this value back into the volume formula:

\[
V = \frac{1}{3} \pi (192)
\]

Now compute \( \frac{192}{3} \):

\[
\frac{192}{3} = 64
\]

Thus, the volume of the cone is:

\[
V = 64\pi
\]

If we want a numerical approximation, we can use \( \pi \approx 3.14 \):

\[
V \approx 64 \times 3.14 = 200.96
\]

Therefore, the volume of the feed container is approximately:

\[
\boxed{200.96} \text{ cubic feet}
\]

And the exact volume is:

\[
\boxed{64\pi} \text{ cubic feet}
\]