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.
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
3 answers
bot that wrong
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.
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.
1 answer