What is the surface area, in square centimeters, of a cone with a diameter of 12 feet and a slant height of 14 feet? Use 3.14 for pi and round to the nearest tenth
To find the surface area of a cone, we need to find the lateral surface area and add the base area.
The lateral surface area of a cone can be found using the formula $A = \pi r L$, where $r$ is the radius of the base and $L$ is the slant height of the cone.
The radius of the base is half the diameter, so $r = \frac{12}{2} = 6$ feet.
Substituting the values into the formula, we get $A = 3.14 \cdot 6 \cdot 14 = 263.52$ square feet (rounding to the nearest tenth).
The base area of a cone can be found using the formula $A = \pi r^2$, where $r$ is the radius of the base.
The radius is also 6 feet, so $A = 3.14 \cdot 6^2 = 3.14 \cdot 36 = 113.04$ square feet (rounding to the nearest hundredth).
The total surface area is the sum of the lateral surface area and the base area, so $263.52 + 113.04 = 376.56$ square feet (rounding to the nearest hundredth).
Since 1 foot is approximately equal to 30.48 centimeters, we can convert the surface area to square centimeters.
$376.56 \text{ square feet} \approx 376.56 \cdot (30.48)^2 \text{ square centimeters} \approx 109758.08$ square centimeters (rounding to the nearest hundredth).
Therefore, the surface area of the cone is approximately $\boxed{109758.08}$ square centimeters.