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)
To find the surface area of the cone, we need to find the lateral area of the cone and the area of the base.
The lateral area of a cone can be calculated using the formula:
Lateral area = π × radius × slant height
The slant height is given as 14 feet. The radius of the cone is half of the diameter, so the radius is 12 feet/2 = 6 feet.
Lateral area = 3.14 × 6 feet × 14 feet
= 263.04 square feet
The area of the base of the cone is given by the formula:
Area of the base = π × radius^2
Area of the base = 3.14 × (6 feet)^2
= 3.14 × 36 square feet
= 113.04 square feet
The total surface area of the cone is the sum of the lateral area and the area of the base:
Surface area = Lateral area + Area of the base
= 263.04 square feet + 113.04 square feet
= 376.08 square feet
Rounding to the nearest tenth, the surface area of the cone is 376.1 square feet.