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) cubic millimeters

Answer 1

The volume \( V \) of a cone can be calculated using the formula:

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

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

1. First, we need to determine the radius \( r \) of the base. The diameter of the cone is given as 14 millimeters, so the radius \( r \) is half of the diameter:

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

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

3. Now, we can substitute the values of \( r \) and \( h \) into the volume formula:

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

4. Calculate \( 7^2 \):

\[ 7^2 = 49 \]

5. Substitute this value into the volume formula:

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

6. Calculate \( 49 \times 12 \):

\[ 49 \times 12 = 588 \]

7. Now substitute back into the volume equation:

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

8. Next, calculate \( 3.14 \times 588 \):

\[ 3.14 \times 588 = 1847.52 \]

9. Finally, divide by 3:

\[ V = \frac{1847.52}{3} \approx 615.84 \]

Therefore, the volume of the cone is approximately:

\[ \boxed{615.84} \text{ cubic millimeters} \]