Final answer:
To calculate the surface area of a cone, the area of the base (a circle) and the lateral surface area must be found. The slant height is calculated using the Pythagorean theorem, giving us the exact total surface area as 144π units².
Step-by-step explanation:
To calculate the surface area of a cone, we use two different parts: the base area and the lateral (side) surface area. The base of the cone is a circle with radius r, so its area is given by the formula πr². The lateral surface area is given by the formula πrℓ where ℓ represents the slant height of the cone. For a right cone, the slant height can be found using the Pythagorean theorem because the slant height (ℓ), the height (h), and the radius (r) form a right triangle. Therefore, ℓ = √(r² + h²).
In this case, r = 8 units and h = 6 units, so the slant height ℓ = √(8² + 6²) = √(64 + 36) = √100 = 10 units. Now we can calculate the total surface area.
The base area Abase = πr² = π × 8² = 64π.
The lateral surface area Alateral = πrℓ = π × 8 × 10 = 80π.
The exact total surface area Atotal = Abase + Alateral = 64π + 80π = 144π units².
Therefore, the precise surface area of the cone is 144π units².