To find the surface area of a cone, you can use the formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where:
- \( r \) is the radius,
- \( l \) is the slant height of the cone.
First, we need to calculate the slant height \( l \) using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle where one leg is the height of the cone and the other leg is the radius.
The formula for the slant height is:
\[ l = \sqrt{r^2 + h^2} \]
Given:
- \( r = 11 \) in
- \( h = 14 \) in
Now calculating \( l \):
\[ l = \sqrt{11^2 + 14^2} = \sqrt{121 + 196} = \sqrt{317} \]
Calculating \( \sqrt{317} \):
\[ l \approx 17.78 \text{ in (rounded to two decimal places)} \]
Now we substitute \( r \) and \( l \) into the surface area formula:
\[ \text{Surface Area} = \pi r (r + l) \] \[ = 3.14 \times 11 \times (11 + 17.78) \] \[ = 3.14 \times 11 \times 28.78 \] \[ = 3.14 \times 11 \times 28.78 \approx 3.14 \times 316.58 \approx 995.43 \]
Now, rounding to the nearest whole number, the surface area of the cone is:
\[ \text{Surface Area} \approx 995 \text{ square inches} \]
Thus, the final answer is:
\[ \boxed{995} \]