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 know the slant height and the radius of the cone. The slant height is 14 feet, which is the hypotenuse of a right triangle formed by the height and the radius of the cone.
Using the Pythagorean theorem, we can find the height of the cone:
height^2 + radius^2 = slant height^2
height^2 + (diameter/2)^2 = slant height^2
height^2 + (12/2)^2 = 14^2
height^2 + 6^2 = 14^2
height^2 + 36 = 196
height^2 = 196 - 36
height^2 = 160
height = √160
height ≈ 12.65 feet
Now, we can calculate the surface area of the cone:
base area = π * radius^2
base area = 3.14 * (12/2)^2
base area = 3.14 * 6^2
base area ≈ 113.04 square centimeters
slant height area = π * radius * slant height
slant height area = 3.14 * 6 * 14
slant height area ≈ 263.52 square centimeters
total surface area = base area + slant height area
total surface area ≈ 113.04 + 263.52
total surface area ≈ 376.56 square centimeters
Therefore, the surface area of the cone is approximately 376.6 square centimeters.