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.(1 point)
in square meters
To solve for the surface area of the cone, we need to find the radius of the base and the lateral surface area.
First, we need to convert the diameter from feet to centimeters:
12 feet = 12 * 30.48 = 365.76 cm
The radius is half the diameter:
radius = 365.76 cm / 2 = 182.88 cm
Next, we calculate the lateral surface area using the formula:
lateral surface area = π * radius * slant height
lateral surface area = 3.14 * 182.88 cm * 14 ft = 3.14 * 182.88 cm * (14 ft * 30.48 cm/ft) = 23917.8912 cm²
Rounded to the nearest tenth, the surface area of the cone is approximately 23917.9 cm².