Question

A cone-shaped container on a farm is used for storing animal feed. The container has a radius of 6 feet and a height of 14 feet. What volume of feed, in cubic feet, can the container store? Round to the nearest hundredth

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 of the base of the cone,
- \( h \) is the height of the cone, and
- \( \pi \) is approximately \( 3.14159 \).

Given:
- \( r = 6 \) feet,
- \( h = 14 \) feet.

First, we calculate \( r^2 \):

\[
r^2 = 6^2 = 36
\]

Then, we substitute the values into the volume formula:

\[
V = \frac{1}{3} \pi (36) (14)
\]

Now, calculate \( 36 \times 14 \):

\[
36 \times 14 = 504
\]

Substituting this back into the formula gives:

\[
V = \frac{1}{3} \pi (504)
\]

Calculating \( \frac{504}{3} \):

\[
\frac{504}{3} = 168
\]

Now substitute \( 168 \) into the volume formula:

\[
V = 168 \pi
\]

Using \( \pi \approx 3.14159 \):

\[
V \approx 168 \times 3.14159 \approx 526.78872
\]

Rounding to the nearest hundredth, the volume of feed the container can store is:

\[
\boxed{526.79} \text{ cubic feet}
\]