Question

Cones, Cylinders, & Spheres Unit Test
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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. What volume of feed, in cubic feet, can the container store? Round your answer to the nearest hundredth. Use 3.14 for π
.(1 point)
cubic feet

Answer 1

To calculate the volume of a cone, we use the formula:

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

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone, and
- \( \pi \) is approximately 3.14.

Given:
- \( r = 4 \) feet,
- \( h = 12 \) feet,
- \( \pi = 3.14 \).

Now we can plug in the values:

\[
V = \frac{1}{3} \times 3.14 \times (4^2) \times 12
\]

Calculating \( 4^2 \):

\[
4^2 = 16
\]

Now, substitute that into the formula:

\[
V = \frac{1}{3} \times 3.14 \times 16 \times 12
\]

Now calculate \( 16 \times 12 \):

\[
16 \times 12 = 192
\]

Now, substitute that back into the equation:

\[
V = \frac{1}{3} \times 3.14 \times 192
\]

Now, calculate \( 3.14 \times 192 \):

\[
3.14 \times 192 = 602.88
\]

Now calculate \( \frac{1}{3} \times 602.88 \):

\[
V = 200.96
\]

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

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