To find the surface area of a cone, we can use the formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where \( r \) is the radius, and \( l \) is the slant height.
-
Convert the diameter to the radius: Given the diameter is 12 feet, the radius \( r \) is:
\[ r = \frac{12}{2} = 6 \text{ feet} \]
-
Use the slant height: The slant height \( l \) is given as 14 feet.
-
Calculate the surface area in square feet: Plugging the values into the surface area formula:
\[ \text{Surface Area} = 3.14 \times 6 \times (6 + 14) \]
First, calculate \( 6 + 14 \):
\[ 6 + 14 = 20 \]
Now substitute back into the surface area formula:
\[ \text{Surface Area} = 3.14 \times 6 \times 20 \]
Calculate \( 3.14 \times 6 = 18.84 \), then:
\[ \text{Surface Area} = 18.84 \times 20 = 376.8 \text{ square feet} \]
-
Convert square feet to square centimeters: There are \( 929.0304 \) square centimeters in one square foot. Therefore, to convert the surface area:
\[ \text{Surface Area in cm}^2 = 376.8 \times 929.0304 \]
Performing the multiplication:
\[ \text{Surface Area in cm}^2 = 350,654.30912 \text{ square centimeters} \]
-
Round to the nearest tenth:
Rounding \( 350,654.30912 \) gives:
\[ 350,654.3 \text{ square centimeters} \]
Thus, the final answer is:
\[ \boxed{350654.3} \text{ square centimeters} \]