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.
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
1 answer