To calculate the surface area of a cone, we can use the formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height,
- \( \pi \) is approximately \( 3.14 \).
- First, we need to find the radius. The diameter of the cone is given as 12 feet, so the radius \( r \) will be:
\[ r = \frac{\text{diameter}}{2} = \frac{12 \text{ ft}}{2} = 6 \text{ ft} \]
-
The slant height \( l \) is given as 14 ft.
-
Now, we can substitute the values of \( r \) and \( l \) into the surface area formula:
\[ \text{Surface Area} = \pi r (r + l) = 3.14 \times 6 \text{ ft} \times (6 \text{ ft} + 14 \text{ ft}) \]
- Calculate \( r + l \):
\[ r + l = 6 \text{ ft} + 14 \text{ ft} = 20 \text{ ft} \]
- Now substitute this into the surface area formula:
\[ \text{Surface Area} = 3.14 \times 6 \text{ ft} \times 20 \text{ ft} \]
- Calculate the surface area:
\[ \text{Surface Area} = 3.14 \times 6 \times 20 = 3.14 \times 120 = 376.8 \text{ ft}^2 \]
- Finally, since the question asks for the surface area in square centimeters, we need to convert square feet to square centimeters. We know that:
\[ 1 \text{ ft}^2 = 929.0304 \text{ cm}^2 \]
So:
\[ \text{Surface Area in cm}^2 = 376.8 \text{ ft}^2 \times 929.0304 \text{ cm}^2/\text{ft}^2 \]
Calculating this:
\[ \text{Surface Area in cm}^2 \approx 376.8 \times 929.0304 \approx 350,113.78 \text{ cm}^2 \]
Thus, the surface area of the cone is approximately:
\[ \boxed{350,113.78 \text{ cm}^2} \]