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:

$$\boxed{{\displaystyle 615.84}}\text{ cubic millimeters}$$