Final answer:
To calculate the surface area of a cone with a radius of 8 cm and a slant height of 10 cm, we find the lateral surface area and base area using the formulae with π ≈ 3.14, and then sum these areas to get approximately 452.2 cm², which corresponds to answer choice C.
Step-by-step explanation:
The surface area of a cone can be found using the formula for the lateral or side area plus the area of the base. The lateral surface area is given by the formula Alateral = πrl, where r is the radius and l is the slant height. The formula for the area of the circular base is Abase = πr². We are given the radius (r) is 8 cm, and the slant height (l) is 10 cm. Using π ≈ 3.14, we calculate the following:
- Lateral Surface Area: Alateral = π*8 cm*10 cm ≈ 3.14*8*10 = 251.2 cm²
- Base Area: Abase = π*8 cm² ≈ 3.14*64 = 201 cm²
Adding these two areas together gives us the total surface area of the cone: Atotal = Alateral + Abase = 251.2 cm² + 201 cm² ≈ 452.2 cm². Therefore, the correct answer is C. 452.2 cm², to the nearest tenth of a square centimeter.