What is the surface area in the square centimeters of a cone with a diameter of 12 feet and a slant height of 14?
The first step is to find the radius of the cone. Since the diameter is 12 feet, the radius is half of this, or 6 feet.
Next, we can use the formula for the lateral surface area of a cone, which is given by the formula $A = \pi r l$, where $r$ is the radius and $l$ is the slant height.
Plugging in the values we have, we get $A = \pi (6)(14) = 84 \pi$.
Since we want the surface area in square centimeters, we need to convert from feet to centimeters. There are 30.48 centimeters in a foot, so we multiply the surface area in feet by 30.48 to get the surface area in centimeters.
$84 \pi \cdot 30.48 = 2562 \pi$.
Rounding to the nearest whole number, we have a surface area of approximately $\boxed{8052}$ square centimeters.