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. ANSWERR BOTT
To find the surface area of a cone, we need to calculate the area of the base and the lateral surface area.
First, let's find the radius of the base (since we were given the diameter).
The diameter of the cone is 12 feet, so the radius is 12/2 = <<12/2=6>>6 feet.
The base of the cone is a circle, so its area is given by the formula: A = πr^2, where A is the area and r is the radius.
A = 3.14 * 6^2 = 3.14 * 36 = 113.04 square feet.
Next, let's find the lateral surface area of the cone.
The slant height of the cone is 14 feet. The slant height, radius, and lateral height of a cone form a right triangle. We can use the Pythagorean theorem to find the lateral height.
The lateral height squared (h) is equal to the slant height squared (l) minus the radius squared (r).
h^2 = l^2 - r^2
h^2 = 14^2 - 6^2
h^2 = 196 - 36
h^2 = 160
Taking the square root of both sides, we find h = √160 ≈ 12.65 feet
The lateral surface area (LA) of the cone is given by the formula: LA = πrl, where r is the radius and l is the slant height.
LA = 3.14 * 6 * 14 = 263.52 square feet.
Finally, we can find the total surface area (SA) of the cone by adding the base area and the lateral surface area.
SA = A + LA
SA = 113.04 + 263.52
SA ≈ 376.56 square feet.
Converting the surface area to square centimeters, we multiply by the conversion factor: 1 square foot = 929.03 square centimeters.
SA ≈ 376.56 * 929.03 ≈ 349944.89 square centimeters.
Therefore, the surface area of the cone is approximately 349944.9 square centimeters.
bot that wrong
To find the surface area of a cone, you need to calculate the lateral surface area and the base area, and then add them together.
First, let's calculate the slant height using the Pythagorean theorem. The slant height, base radius, and height of a cone form a right triangle.
Since the diameter is 12 feet, the radius is half of that, which is 12/2 = 6 feet.
Using the Pythagorean theorem, we have:
slant height^2 = height^2 + radius^2
14^2 = height^2 + 6^2
196 = height^2 + 36
height^2 = 196 - 36
height^2 = 160
height = √160
height ≈ 12.65 feet
Now that we have both the height and the radius, we can calculate the lateral surface area and the base area.
The lateral surface area of a cone is given by the formula:
lateral surface area = π × radius × slant height
lateral surface area = 3.14 × 6 × 14
lateral surface area ≈ 263.76 square feet
The base area of the cone is given by the formula:
base area = π × radius^2
base area = 3.14 × 6^2
base area ≈ 113.04 square feet
Finally, to find the total surface area, you add the lateral surface area and the base area:
total surface area ≈ lateral surface area + base area
total surface area ≈ 263.76 + 113.04
total surface area ≈ 376.80 square feet
Therefore, the surface area of the cone is approximately 376.8 square feet.
Apologies for the confusion.
To find the surface area of a cone, we need to calculate the area of the base and the lateral surface area.
First, let's find the radius of the base (since we were given the diameter).
The diameter of the cone is 12 feet, so the radius is 12/2 = 6 feet.
The base of the cone is a circle, so its area is given by the formula: A = πr^2, where A is the area and r is the radius.
A = 3.14 * 6^2 = 3.14 * 36 = 113.04 square feet.
Next, let's find the lateral surface area of the cone.
The slant height of the cone is 14 feet. The slant height, radius, and lateral height of a cone form a right triangle. We can use the Pythagorean theorem to find the lateral height.
The lateral height squared (h) is equal to the slant height squared (l) minus the radius squared (r).
h^2 = l^2 - r^2
h^2 = 14^2 - 6^2
h^2 = 196 - 36
h^2 = 160
Taking the square root of both sides, we find h = √160 ≈ 12.65 feet
The lateral surface area (LA) of the cone is given by the formula: LA = πrl, where r is the radius and l is the slant height.
LA = 3.14 * 6 * 14 = 263.52 square feet.
Finally, we can find the total surface area (SA) of the cone by adding the base area and the lateral surface area.
SA = A + LA
SA = 113.04 + 263.52
SA = 376.56 square feet.
Therefore, the surface area of the cone is approximately 376.56 square feet.