Final answer:
The surface area of a cone with a radius of 8 and a slant height of 13.6 is approximately 1286.848 square units.
Step-by-step explanation:
The surface area of a cone can be found using the formula for the lateral (or side) surface area plus the area of the base. The lateral surface area of a cone is πrl, where 'r' is the radius and 'l' is the slant height. The area of the base is πr², where 'r' is the radius. Given the radius 'r' is 8 and the slant height 'l' is 13.6, we first calculate:
- Lateral surface area = π * r * l = π * 8 * 13.6
- Area of base = π * r² = π * 8²
After calculating these two areas, we add them together to get the total surface area of the cone.
The lateral surface area is approximately 345.6π and the base area is 64π. So the total surface area is 409.6π, which is about 1286.848 when π is approximated to 3.14.