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

1 answer

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 of the base and \( h \) is the height of the cone.

Given:

  • Radius \( r = 4 \) feet
  • Height \( h = 12 \) feet

Using the formula:

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

Calculating \( (4)^2 \):

\[ (4)^2 = 16 \]

Now substituting back into the volume formula:

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

Calculating \( 16 \times 12 \):

\[ 16 \times 12 = 192 \]

Thus, the volume becomes:

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

Now dividing \( 192 \) by \( 3 \):

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

So, the volume is:

\[ V = 64 \pi \]

Approximating \( \pi \) as \( 3.14 \):

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

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