if the height of the base equals 9.3, the base equals 6, and the slant height equals 8. What is the surface area?
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.