To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
In this case, the radius \( r \) is 13 inches and the height \( h \) is 27 inches. Plugging in these values:
\[ V = \frac{1}{3} \pi (13)^2 (27) \]
First, calculate \( (13)^2 \):
\[ (13)^2 = 169 \]
Now substitute back into the volume formula:
\[ V = \frac{1}{3} \pi (169)(27) \]
Next, calculate \( 169 \times 27 \):
\[ 169 \times 27 = 4563 \]
Now substitute this back into the equation for volume:
\[ V = \frac{1}{3} \pi (4563) \]
Now, divide \( 4563 \) by 3:
\[ \frac{4563}{3} = 1521 \]
So the volume becomes:
\[ V = 1521\pi \]
Finally, using the approximate value of \( \pi \) (which is about 3.14), we can find a numerical value for the volume:
\[ V \approx 1521 \times 3.14 \]
Calculating this:
\[ V \approx 4778.94 \]
Thus, the volume of the cone is approximately:
\[ \boxed{1521\pi} \text{ cubic inches} \]
If you want to express this numerically:
\[ \boxed{4778.94} \text{ cubic inches} \] (This is an approximation)