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.

Answer 1

To begin, let's calculate the volume of the cone-shaped container using the formula for the volume of a cone:

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

Where:
- \( V \) is the volume,
- \( r \) is the radius, and
- \( h \) is the height.

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

Now plug in the values:

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

Calculating \( r^2 \):

\[
(4)^2 = 16
\]

So, we substitute that value into the equation:

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

Now multiply \( 16 \) and \( 12 \):

\[
16 \times 12 = 192
\]

Now substitute that back in:

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

Calculating \( \frac{192}{3} \):

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

So now we have:

\[
V = 64\pi
\]

Now, if you want to find a numerical value for the volume, you can substitute \( \pi \approx 3.14 \):

\[
V \approx 64 \times 3.14 \approx 200.96 \text{ cubic feet}
\]

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

\[
V = 64\pi \text{ cubic feet} \quad \text{or approximately} \quad 200.96 \text{ cubic feet}
\]