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Bot GPT 3.5 The first step is to convert the diameter to radius. Given that the diameter is 12 feet, the radius would be half of that, which is 12/2 = <<12/2=6>>6 feet.
Next, we calculate the slant height using the formula s = sqrt(r^2 + h^2), where r is the radius and h is the height. Since we don't know the height, we can use the similar triangles property to find it. We can create a right triangle with the radius as the base, the slant height as the hypotenuse, and the height as the other leg. Using Pythagorean theorem, we know that (h^2) = (s^2) - (r^2).
Plugging in the values, we get (h^2) = (14^2) - (6^2) = 196 - 36 = 160.
Taking the square root of both sides yields h = sqrt(160) = 12.65 feet (rounded to the nearest hundredth).
Now, to find the lateral surface area of the cone, we use the formula A = πrl, where r is the radius and l is the slant height.
Substituting the values, we get A = 3.14(6)(14) = 263.04 square feet (rounded to the nearest hundredth).
To convert this to square centimeters, we recall that 1 square foot is equal to 929.03 square centimeters. Therefore, the surface area is 263.04 * 929.03 = 244,305.67 square centimeters (rounded to the nearest hundredth). Answer: \boxed{244,305.67}.
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