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

1 answer

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:

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