What is the surface area in square centimeters of a cone with a diameter of 12 feet and a slant height of 14 feet?
To find the surface area of a cone, we need to find the lateral surface area and the base area.
The lateral surface area of a cone can be found using the formula:
Lateral surface area = π × radius × slant height
We need to convert the diameter of 12 feet to radius by dividing it by 2:
Radius = Diameter/2 = 12 feet/2 = 6 feet
The slant height is given as 14 feet.
Lateral surface area = π × 6 feet × 14 feet
Lateral surface area = 84π square feet
The base area of a cone can be found using the formula:
Base area = π × radius^2
Base area = π × (6 feet)^2
Base area = 36π square feet
The total surface area of the cone is the sum of the lateral surface area and the base area:
Total surface area = Lateral surface area + Base area
Total surface area = 84π square feet + 36π square feet
Total surface area = 120π square feet
To convert to square centimeters, we need to multiply by the conversion factor:
1 square foot = 929.03 square centimeters
Total surface area = 120π square feet × 929.03 square centimeters/square foot
Total surface area ≈ 350,366.8 square centimeters
Therefore, the surface area of the cone is approximately 350,366.8 square centimeters.