Question
if the height of the base equals 9.3, the base equals 6, and the slant height equals 8. What is the surface area?
Answers
GPT 3.5
To calculate the surface area of a cone, we need to find the lateral area and the base area, and then add them together.
The formula for the lateral area of a cone is L = πrℓ, where r is the radius and ℓ is the slant height.
Given that the base equals 6, we can find the radius of the cone by dividing the base by 2: r = 6 / 2 = 3.
Given that the slant height equals 8, and the radius equals 3, we can calculate the lateral area: L = π(3)(8) = 24π.
Next, we need to calculate the base area. The formula for the base area of a cone is A = πr^2.
Given that the radius is 3, we can calculate the base area: A = π(3)^2 = 9π.
Finally, we calculate the surface area by adding the lateral area and the base area: 24π + 9π = 33π.
Therefore, the surface area of the cone is 33π.
The formula for the lateral area of a cone is L = πrℓ, where r is the radius and ℓ is the slant height.
Given that the base equals 6, we can find the radius of the cone by dividing the base by 2: r = 6 / 2 = 3.
Given that the slant height equals 8, and the radius equals 3, we can calculate the lateral area: L = π(3)(8) = 24π.
Next, we need to calculate the base area. The formula for the base area of a cone is A = πr^2.
Given that the radius is 3, we can calculate the base area: A = π(3)^2 = 9π.
Finally, we calculate the surface area by adding the lateral area and the base area: 24π + 9π = 33π.
Therefore, the surface area of the cone is 33π.