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 if necessary
To find the surface area of a cone, we need to find the lateral area and the base area.
The lateral area of a cone is given by the formula L = π*r*l, where r is the radius of the base and l is the slant height.
Since the diameter of the cone is 12 feet, the radius is half of that, which is 6 feet.
We are given that the slant height is 14 feet.
Therefore, the lateral area is L = 3.14*6*14 = 263.04 square feet.
The base area of a cone is given by the formula B = π*r^2.
Using the radius we found earlier, the base area is B = 3.14*6^2 = 113.04 square feet.
The surface area of the cone is the sum of the lateral area and the base area, so the total surface area is:
S = L + B = 263.04 + 113.04 = 376.08 square feet.
Since we want the answer in square centimeters, and 1 square foot is equal to 929.03 square centimeters,
the surface area of the cone is 376.08*929.03 = 349,182.52 square centimeters.
Therefore, the surface area of the cone is approximately 349,182.5 square centimeters.