What is the volume, in cubic millimeters, of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth.(1 point)

cubic millimeters
hight 12mm base 14mm

1 answer

To find the volume of a cone, you can 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 a constant approximately equal to 3.14.

Given the height \( h = 12 \) mm and the diameter of the base \( d = 14 \) mm, we can calculate the radius:

\[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ mm} \]

Now substitute the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]

Calculating \( 7^2 \):

\[ 7^2 = 49 \]

Now substituting that back in:

\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]

Calculating \( 49 \times 12 \):

\[ 49 \times 12 = 588 \]

Now substituting that back in:

\[ V = \frac{1}{3} \times 3.14 \times 588 \]

Calculating \( 3.14 \times 588 \):

\[ 3.14 \times 588 = 1847.92 \]

Now dividing by 3:

\[ V = \frac{1847.92}{3} = 615.9733333 \]

Rounding to the nearest hundredth:

\[ V \approx 615.97 \]

Thus, the volume of the cone is approximately \( \boxed{615.97} \) cubic millimeters.