Question

A cone-shaped container on a farm is used for storing animal feed. The container has a radius of 4 feet and a height of 12 feet. (1 point)
The volume of feed, in cubic feet, this container can store is
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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 and \( h \) is the height of the cone.

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

We can substitute these values into the formula:

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

Calculating \( 4^2 \):

\[
4^2 = 16
\]

Now substitute that back into the volume formula:

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

Now, multiply \( 16 \) by \( 12 \):

\[
16 \times 12 = 192
\]

So now we have:

\[
V = \frac{1}{3} \pi (192) = \frac{192}{3} \pi = 64 \pi
\]

To find the approximate numerical value, we can use \( \pi \approx 3.14 \):

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

Thus, the volume of the cone-shaped container is approximately:

\[
V \approx 200.96 \text{ cubic feet}
\]

In summary, the volume of feed this container can store is \( 64\pi \) cubic feet, or approximately 200.96 cubic feet.