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 3.144 pi and round to the nearest 10th if necessary
First, we need to convert the diameter and slant height from feet to centimeters.
12 feet = 12 * 30.48 = <<12*30.48=365.76>>365.76 cm (rounded to the nearest hundredth).
14 feet = 14 * 30.48 = <<14*30.48=426.72>>426.72 cm (rounded to the nearest hundredth).
Next, we need to calculate the radius of the cone. The radius is half the diameter, so the radius is 365.76 cm / 2 = <<365.76/2=182.88>>182.88 cm (rounded to the nearest hundredth).
Using the formula for the lateral surface area of a cone, we have:
Lateral Surface Area = π * r * l
where r is the radius and l is the slant height.
Lateral Surface Area = 3.144 * 182.88 * 426.72
Lateral Surface Area ≈ 236,975.793 cm² (rounded to the nearest tenth).
Therefore, the surface area of the cone is approximately 236,975.8 square centimeters.