Erik measures a cone with a radius of 12 feet and a height that is half the length of the radius. What is the volume of Erik’s cone? Use 3.14 for pi and express your answer to the nearest tenth of a cubic foot.

1 answer

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

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

where \( r \) is the radius and \( h \) is the height of the cone.

Given:

  • The radius \( r = 12 \) feet.
  • The height \( h \) is half the length of the radius. Therefore,

\[ h = \frac{1}{2} \times r = \frac{1}{2} \times 12 = 6 \text{ feet}. \]

Now, we can substitute the radius and height into the volume formula:

\[ V = \frac{1}{3} \pi (12)^2 (6) \]

Calculating \( (12)^2 \):

\[ (12)^2 = 144 \]

Now, substituting this value into the volume formula:

\[ V = \frac{1}{3} \pi (144)(6) \]

Calculating \( 144 \times 6 \):

\[ 144 \times 6 = 864 \]

Now substituting this back into the volume formula:

\[ V = \frac{1}{3} \pi (864) \]

Using \( \pi = 3.14 \):

\[ V = \frac{1}{3} \times 3.14 \times 864 \]

Calculating \( \frac{1}{3} \times 864 \):

\[ \frac{1}{3} \times 864 = 288 \]

Now substituting this into the formula:

\[ V = 3.14 \times 288 \]

Calculating \( 3.14 \times 288 \):

\[ 3.14 \times 288 = 904.32 \]

Finally, rounding \( 904.32 \) to the nearest tenth:

\[ V \approx 904.3 \text{ cubic feet} \]

Thus, the volume of Erik’s cone is

\[ \boxed{904.3} \text{ cubic feet}. \]