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 the cone, we need to find the lateral surface area and the base area separately and then add them together.
The lateral surface area of a cone can be found using the formula A = πrs , where r is the radius of the base and s is the slant height.
Since the diameter is given as 12 feet, the radius is half of that, which is 6 feet.
The lateral surface area is then A = 3.14(6)(14) = 263.04 square feet.
To find the base area, we use the formula A = πr^2.
The radius is still 6 feet, so the base area is A = 3.14(6)^2 = 113.04 square feet.
Now we can find the total surface area by adding the lateral surface area and the base area:
263.04 + 113.04 = 376.08
Therefore, the surface area of the cone is 376.08 square feet.
wrong
yeah wrong
To find the surface area of a cone, you need to determine the curved surface area, also known as the lateral surface area, and the base area. You can calculate the curved surface area using the formula A = πrs, where A represents the curved surface area, π represents the value of pi, r represents the radius, and s represents the slant height. The formula for the base area of a cone is A = πr^2, where A represents the base area, and r represents the radius.
First, you need to convert the given measurements to the same units. Since the diameter is given in feet and the final answer should be in square centimeters, let's convert the measurements to centimeters.
1 foot = 30.48 centimeters (approximately)
Therefore, the diameter of 12 feet is equal to 12 × 30.48 = 365.76 centimeters.
The radius of the cone is half of the diameter, so the radius is 365.76 / 2 = 182.88 centimeters.
Now, let's calculate the curved surface area:
Curved Surface Area (A) = π × radius (r) × slant height (s)
Curved Surface Area (A) = 3.14 × 182.88 × 14
Curved Surface Area (A) ≈ 8019.8 square centimeters (rounded to the nearest tenth)
Next, let's calculate the base area:
Base Area (A) = π × radius (r)^2
Base Area (A) = 3.14 × 182.88^2
Base Area (A) ≈ 104643.5 square centimeters (rounded to the nearest tenth)
Finally, to find the total surface area of the cone, you need to add the curved surface area and the base area:
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area ≈ 8019.8 + 104643.5
Total Surface Area ≈ 112663.3 square centimeters (rounded to the nearest tenth)
Therefore, the surface area of the given cone is approximately 112663.3 square centimeters.