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 centimeters
To find the surface area of a cone, we need to find the curved surface area and the base area separately and then add them together.
The curved surface area of a cone is given by the formula:
CSA = π * r * l
where r is the radius of the base and l is the slant height.
First, we need to convert the diameter of the cone from feet to centimeters. 1 foot is equal to 30.48 centimeters. So the diameter of the cone is 12 feet * 30.48 centimeters/foot = 365.76 centimeters.
The radius of the base of the cone is half the diameter, so r = 365.76 centimeters / 2 = 182.88 centimeters.
Plugging in the values into the formula:
CSA = 3.14 * 182.88 cm * 14 cm = 8075.59 square centimeters.
Next, we need to calculate the base area of the cone. The base is a circle, so its area can be found using the formula:
Base Area = π * r^2
Plugging in the values:
Base Area = 3.14 * (182.88 cm)^2 = 314113.44 square centimeters.
Finally, we can calculate the surface area by adding the curved surface area and base area:
Surface Area = CSA + Base Area = 8075.59 square centimeters + 314113.44 square centimeters = 322189.03 square centimeters.
Rounded to the nearest tenth, the surface area of the cone is approximately 322189.0 square centimeters.