Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches. Round your answer to the nearest hundredth..
The volume of a cone can be calculated using the formula $V=\frac{1}{3}\pi r^2h$, where $r$ represents the radius and $h$ represents the height.
Substituting in the given values, the volume of the cone is $\frac{1}{3}\pi(13^2)(27) \approx \frac{1}{3}(169\cdot27)\pi \approx \frac{1}{3}(4563)\pi$ cubic inches.
To round the answer to the nearest hundredth, we need to have a decimal approximation of $\pi$.
The commonly used approximation for $\pi$ is 3.14.
Therefore, the volume of the cone is approximately $\frac{1}{3}(4563)(3.14) \approx \frac{1}{3}(14322.42) \approx 4774.14$ cubic inches.
So, the volume of the cone is approximately $\boxed{4774.14}$ cubic inches.