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)
square centimeters
First, we need to convert the diameter from feet to centimeters. Since 1 foot is equal to 30.48 centimeters, the diameter of the cone is 12 feet * 30.48 centimeters/foot = 365.76 centimeters.
Next, we can use the slant height and the radius to find the height of the cone. The slant height is the hypotenuse of a right triangle, with the radius as one of the legs. We can use the Pythagorean theorem to find the height. Let's call the radius r and the height h.
From the Pythagorean theorem, we have:
r^2 + h^2 = slant height^2
r^2 + h^2 = 14 feet * 30.48 centimeters/foot = 426.72 centimeters
Since the diameter is equal to twice the radius, we have:
r = diameter/2 = 365.76 centimeters/2 = 182.88 centimeters
Substituting this into the equation above, we have:
(182.88 centimeters)^2 + h^2 = 426.72 centimeters^2
33415.3344 square centimeters + h^2 = 426.72 square centimeters^2
h^2 = 426.72 square centimeters^2 - 33415.3344 square centimeters
h^2 = 39376.8656 square centimeters
h = √(39376.8656 square centimeters) ≈ 198.4 square centimeters
Now, we can calculate the surface area of the cone. The formula for the surface area of a cone is given by:
Surface Area = π * r * (r + slant height)
Surface Area = 3.14 * 182.88 square centimeters * (182.88 square centimeters + 426.72 square centimeters)
Surface Area = 3.14 * 182.88 square centimeters * 609.6 square centimeters
Surface Area ≈ 347844.2272 square centimeters
Rounding to the nearest tenth, the surface area of the cone is ≈ 347844.2 square centimeters.