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 of the base,
- \( h \) is the height of the cone,
- \( \pi \) is approximately \( 3.14159 \).
Given:
- Radius \( r = 13 \) cm
- Height \( h = 27 \) cm
Plugging in the values:
\[ V = \frac{1}{3} \pi (13)^2 (27) \]
Calculating \( (13)^2 \):
\[ (13)^2 = 169 \]
Now substitute back into the equation:
\[ V = \frac{1}{3} \pi (169)(27) \]
Calculating \( 169 \times 27 \):
\[ 169 \times 27 = 4563 \]
Now substitute this back into the volume equation:
\[ V = \frac{1}{3} \pi (4563) \]
Dividing by 3:
\[ \frac{4563}{3} = 1521 \]
Thus:
\[ V = 1521 \pi \]
To find a numerical approximation, use \( \pi \approx 3.14159 \):
\[ V \approx 1521 \times 3.14159 \approx 4779.32 \]
Rounding to the nearest tenth:
\[ \boxed{4779.3} \text{ cm}^3 \]
The volume of the cone is approximately \( 4779.3 \text{ cm}^3 \).