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 and \( h \) is the height of the cone.
Given:
- Radius \( r = 13 \) inches
- Height \( h = 27 \) inches
- Using \( \pi \approx 3.14 \)
Now, substituting the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (13)^2 \times 27 \]
Calculating \( (13)^2 \):
\[ (13)^2 = 169 \]
Now plug that into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 169 \times 27 \]
Calculating \( 169 \times 27 \):
\[ 169 \times 27 = 4563 \]
Now, substituting this back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 4563 \]
Calculating \( 3.14 \times 4563 \):
\[ 3.14 \times 4563 \approx 14317.82 \]
Now, dividing by 3:
\[ V \approx \frac{14317.82}{3} \approx 4772.61 \]
Therefore, the volume of the cone, rounded to the nearest hundredth, is:
\[ \boxed{4772.61} \text{ cubic inches.} \]