What is the volume of this cone? Use π ≈ 3.14 and round your answer to the nearest hundredth. The cone has a radius of 7 meters and a height of 13 meters.

Steps to Solve

1. Find the radius

The diameter of the cone is given as 14 meters. The radius $r$ is half of the diameter.

$r = \frac{14}{2} = 7$ meters

2. State the formula for the volume of a cone

The volume $V$ of a cone is given by the formula:

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

where $r$ is the radius and $h$ is the height.

3. Substitute the given values into the formula

We are given that $h = 13$ meters, $r = 7$ meters, and $\pi \approx 3.14$. Substituting these values into the volume formula gives:

$V = \frac{1}{3} \times 3.14 \times (7)^2 \times 13$

4. Calculate the volume

$V = \frac{1}{3} \times 3.14 \times 49 \times 13$

$V = \frac{1}{3} \times 3.14 \times 637$

$V = \frac{2000.18}{3}$

$V = 666.726666...$

5. Round to the nearest hundredth

Rounding the volume to the nearest hundredth gives:

$V \approx 666.73$ cubic meters