To calculate the surface area of a cone, we can use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height.
Given:
- The diameter of the cone is 12 feet.
- The slant height \( l \) is 14 feet.
First, we need to find the radius \( r \) from the diameter:
\[ r = \frac{\text{diameter}}{2} = \frac{12 \text{ feet}}{2} = 6 \text{ feet} \]
Now, substituting the values into the surface area formula:
- Calculate the area of the base:
\[ \pi r^2 = 3.14 \times (6 \text{ feet})^2 = 3.14 \times 36 \text{ square feet} = 113.04 \text{ square feet} \]
- Calculate the lateral area:
\[ \pi r l = 3.14 \times 6 \text{ feet} \times 14 \text{ feet} \]
\[ = 3.14 \times 84 \text{ square feet} = 263.76 \text{ square feet} \]
- Adding the base area and the lateral area:
\[ \text{Surface Area} = 113.04 \text{ square feet} + 263.76 \text{ square feet} = 376.8 \text{ square feet} \]
Now, convert the surface area from square feet to square centimeters. Since 1 foot is equivalent to 30.48 centimeters, the conversion factor for square feet to square centimeters is:
\[ (30.48 \text{ cm})^2 = 929.0304 \text{ cm}^2 \]
Thus, converting square feet to square centimeters:
\[ \text{Surface Area in cm}^2 = 376.8 \text{ square feet} \times 929.0304 \text{ cm}^2/\text{square foot} \approx 350,222.5 \text{ cm}^2 \]
Finally, rounding to the nearest tenth, the surface area of the cone is:
\[ \boxed{350222.5 , \text{cm}^2} \]