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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

To find the volume \( V \) of a cone, you can use the formula:

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

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

1. Find the radius: The diameter of the base is given as 14 millimeters, so the radius \( r \) is:

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

2. Use the height: The height \( h \) is given as 12 millimeters.

3. Substitute the values into the volume formula:

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

4. Calculate \( r^2 \):

\[ 7^2 = 49 \]

5. Now plug in the values:

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

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

\[ 49 \times 12 = 588 \]

7. Now the volume formula simplifies to:

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

8. Calculate \( 3.14 \times 588 \):

\[ 3.14 \times 588 = 1846.32 \]

9. Finally, divide by 3:

\[ V = \frac{1846.32}{3} = 615.44 \]

So the volume of the cone is:

\[ \boxed{615.44} \text{ cubic millimeters} \]