Use the image to answer the question.

Question

A right cone shows a base diameter of 14 millimeters and a perpendicular height of 12 millimeters. A right angle is formed with the diameter and the height at the center of the circular base.

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

Answer 1

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

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

where:

• \( r \) is the radius of the base,
• \( h \) is the height of the cone.

Given that the diameter of the base is 14 millimeters, we can find the radius:

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

The height \( h \) of the cone is given as 12 millimeters.

Now, we can substitute \( r \), \( h \), and \( \pi \) (given as 3.14) into the volume formula:

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

Calculating \( r^2 \):

\[ (7)^2 = 49 \]

Now substituting this into the volume formula:

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

Calculating \( 49 \times 12 \):

\[ 49 \times 12 = 588 \]

Now substituting this back into the volume calculation:

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

Calculating \( 3.14 \times 588 \):

\[ 3.14 \times 588 = 1847.92 \]

Now dividing by 3:

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

Rounding to the nearest hundredth:

\[ V \approx 615.97 \]

Therefore, the volume of the cone is approximately:

\[ \boxed{615.97} \text{ cubic millimeters} \]