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 don't round to the nearest tenth, 1 point)
square centimeters
To find the surface area of a cone, we need to find the lateral surface area first. The lateral surface area of a cone can be found using the formula:
Lateral Surface Area = π × r × s
Where s is the slant height and r is the radius.
Given that the diameter of the cone is 12 feet, we can find the radius by dividing the diameter by 2:
Radius = 12 ft / 2 = 6 ft
Therefore, the radius of the cone is 6 feet.
Now, substitute the values into the formula:
Lateral Surface Area = π × 6 ft × 14 ft
Lateral Surface Area = 84π ft^2
To find the surface area of the entire cone, we need to add the base area to the lateral surface area.
The base area can be found using the formula:
Base Area = π × r^2
Given that the radius is 6 feet:
Base Area = π × (6 ft)^2
Base Area = 36π ft^2
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 ft^2 + 36π ft^2
Total Surface Area = 120π ft^2
To convert the area to square centimeters, we need to multiply by the conversion factor:
1 ft^2 = 929.03 cm^2
Total Surface Area = 120π ft^2 × 929.03 cm^2/ft^2
Total Surface Area ≈ 111757.21π cm^2
Using the value of pi as 3.14:
Total Surface Area ≈ 352062.862 cm^2
Therefore, the surface area of the cone is approximately 352062.862 square centimeters.