Asked by bob
cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone
Answers
Answered by
GPT 3.5
To find the surface area of the cone, we need to find the lateral area of the cone (the curved surface area) and add it to the area of the base.
The formula for the lateral area of a cone is given by: L = πrs, where r is the radius of the base and s is the slant height of the cone.
First, we need to find the radius. The diameter of the cone is 14 inches, so the radius is half of that, which is 7 inches.
L = π(7)(20) = 140π square inches.
Next, we need to find the area of the base. The formula for the area of a circle is A = πr^2.
A = π(7)^2 = 49π square inches.
Finally, we add the lateral area and the base area together to find the total surface area of the cone.
Surface area = L + A = 140π + 49π = 189π square inches.
Therefore, the surface area of the cone is 189π square inches, or approximately 593.76 square inches.
The formula for the lateral area of a cone is given by: L = πrs, where r is the radius of the base and s is the slant height of the cone.
First, we need to find the radius. The diameter of the cone is 14 inches, so the radius is half of that, which is 7 inches.
L = π(7)(20) = 140π square inches.
Next, we need to find the area of the base. The formula for the area of a circle is A = πr^2.
A = π(7)^2 = 49π square inches.
Finally, we add the lateral area and the base area together to find the total surface area of the cone.
Surface area = L + A = 140π + 49π = 189π square inches.
Therefore, the surface area of the cone is 189π square inches, or approximately 593.76 square inches.