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 answer

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

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

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given:

  • Radius, \( r = 4 \) feet
  • Height, \( h = 12 \) feet
  • \( \pi \approx 3.14 \)

Plugging in these values into the formula:

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

Calculating \( (4)^2 \):

\[ (4)^2 = 16 \]

Now substituting back:

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

Next, calculating \( 16 \times 12 \):

\[ 16 \times 12 = 192 \]

Now substituting this value:

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

Calculating \( 3.14 \times 192 \):

\[ 3.14 \times 192 = 601.44 \]

Now, take one-third of that value:

\[ V = \frac{601.44}{3} = 200.48 \]

Therefore, the volume of feed that the container can store is approximately:

\[ \boxed{200.48} \text{ cubic feet} \]