The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
In this case, the radius \( r = 13 \) cm and the height \( h = 27 \) cm.
Now, we can plug in the 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 we can find the volume:
\[ V = \frac{1}{3} \pi (4563) \]
Calculating \( \frac{4563}{3} \):
\[ \frac{4563}{3} = 1521 \]
Thus, the volume is:
\[ V \approx 1521 \pi \]
Now, to find the numerical value, we use \( \pi \approx 3.14159 \):
\[ V \approx 1521 \times 3.14159 \approx 4777.96339 \]
Rounding to the nearest tenth:
\[ V \approx 4778.0 \]
Therefore, the volume of the cone is approximately:
\[ \boxed{4778.0} \text{ cubic centimeters} \]